ordered pairs in A × B and B × A

Question

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Answer 1

Question

Chapter 2.2, Problem 13E

a.

To determine

To list:ordered pairs in A×B and B×A

a.

Expert Solution

Answer to Problem 13E

A×B={(1,a),(1,e),(1,k),(1,n),(1,r),(3,a),(3,e),(3,k),(3,n),(3,r),(5,a),(5,e),(5,k),(5,n),(5,r)}

B×A={(a,1),(e,1),(k,1),(n,1),(r,1),(a,3),(e,3),(k,3),(n,3),(r,3),(a,5),(e,5),(k,5),(n,5),(r,5)}

Explanation of Solution

Given:

A={1,3,5}

B={a,e,k,n,r}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={1,3,5} and B={a,e,k,n,r}

Then by definition of cross product,

A×B={(1,a),(1,e),(1,k),(1,n),(1,r),(3,a),(3,e),(3,k),(3,n),(3,r),(5,a),(5,e),(5,k),(5,n),(5,r)}

And

B×A={(a,1),(e,1),(k,1),(n,1),(r,1),(a,3),(e,3),(k,3),(n,3),(r,3),(a,5),(e,5),(k,5),(n,5),(r,5)}

b.

To determine

To list: ordered pairs in A×B and B×A

b.

Expert Solution

Answer to Problem 13E

A×B={(1,q),(2,q),({ 1,2},q),(1,{t}),(2,{t}),({ 1,2},{t}),(1,π),(2,π),({ 1,2},π)}

B×A={(q,1),(q,2),(q,{ 1,2}),({t},1),({t},2),({t},{ 1,2}),(π,1),(π,2),(π,{ 1,2})}

Explanation of Solution

Given:

A={1,2,{1,2}}

B={q,{t},π}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={1,2,{1,2}} and B={q,{t},π}

Then by definition of cross product,

A×B={(1,q),(2,q),({ 1,2},q),(1,{t}),(2,{t}),({ 1,2},{t}),(1,π),(2,π),({ 1,2},π)}

And

B×A={(q,1),(q,2),(q,{ 1,2}),({t},1),({t},2),({t},{ 1,2}),(π,1),(π,2),(π,{ 1,2})}

c.

To determine

To list: ordered pairs in A×B and B×A

c.

Expert Solution

Answer to Problem 13E

A×B={(∅,( ∅,{∅})),(∅,{∅}),(∅,( {∅},∅)),({∅},( ∅,{∅})),({∅},{∅}),({∅},( {∅},∅)),({ ∅,{∅}},( ∅,{∅})),({ ∅,{∅}},{∅}),({ ∅,{∅}},( {∅},∅))}

B×A={(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}})}

Explanation of Solution

Given:

A={∅,{∅},{∅,{∅}}}

B={(∅,{∅}),{∅},({∅},∅)}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={∅,{∅},{∅,{∅}}} and B={(∅,{∅}),{∅},({∅},∅)}

Then by definition of cross product,

A×B={(∅,( ∅,{∅})),(∅,{∅}),(∅,( {∅},∅)),({∅},( ∅,{∅})),({∅},{∅}),({∅},( {∅},∅)),({ ∅,{∅}},( ∅,{∅})),({ ∅,{∅}},{∅}),({ ∅,{∅}},( {∅},∅))}

And

B×A={(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}})}

d.

To determine

To list: ordered pairs in A×B and B×A

d.

Expert Solution

Answer to Problem 13E

A×B={((2,4),(4,1)),((3,1),(4,1)),((2,4),(2,3)),((3,1),(2,3))}

B×A={((4,1),(2,4)),((2,3),(2,4)),((4,1),(3,1)),((2,3),(3,1))}

Explanation of Solution

Given:

A={(2,4),(3,1)}

B={(4,1),(2,3)}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={(2,4),(3,1)} and B={(4,1),(2,3)}

Then by definition of cross product,

A×B={((2,4),(4,1)),((3,1),(4,1)),((2,4),(2,3)),((3,1),(2,3))}

And

B×A={((4,1),(2,4)),((2,3),(2,4)),((4,1),(3,1)),((2,3),(3,1))}

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Students have asked these similar questions

2. Consider the ODE u' = ƒ (u) = u² + r where r is a parameter that can take the values r = −1, −0.5, -0.1, 0.1. For each value of r: (a) Sketch ƒ(u) = u² + r and determine the equilibrium points. (b) Draw the phase line. (d) Determine the stability of the equilibrium points. (d) Plot the direction field and some sample solutions,i.e., u(t) (e) Describe how location of the equilibrium points and their stability change as you increase the parameter r. (f) Using the matlab program phaseline.m generate a solution for each value of r and the initial condition u(0) = 0.9. Print and turn in your result for r = −1. Do not forget to add a figure caption. (g) In the matlab program phaseline.m set the initial condition to u(0) = 1.1 and simulate the ode over the time interval t = [0, 10] for different values of r. What happens? Why? You do not need to turn in a plot for (g), just describe what happens.

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Answer 2

Question

Chapter 2.2, Problem 13E

a.

To determine

To list:ordered pairs in A×B and B×A

a.

Expert Solution

Answer to Problem 13E

A×B={(1,a),(1,e),(1,k),(1,n),(1,r),(3,a),(3,e),(3,k),(3,n),(3,r),(5,a),(5,e),(5,k),(5,n),(5,r)}

B×A={(a,1),(e,1),(k,1),(n,1),(r,1),(a,3),(e,3),(k,3),(n,3),(r,3),(a,5),(e,5),(k,5),(n,5),(r,5)}

Explanation of Solution

Given:

A={1,3,5}

B={a,e,k,n,r}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={1,3,5} and B={a,e,k,n,r}

Then by definition of cross product,

A×B={(1,a),(1,e),(1,k),(1,n),(1,r),(3,a),(3,e),(3,k),(3,n),(3,r),(5,a),(5,e),(5,k),(5,n),(5,r)}

And

B×A={(a,1),(e,1),(k,1),(n,1),(r,1),(a,3),(e,3),(k,3),(n,3),(r,3),(a,5),(e,5),(k,5),(n,5),(r,5)}

b.

To determine

To list: ordered pairs in A×B and B×A

b.

Expert Solution

Answer to Problem 13E

A×B={(1,q),(2,q),({ 1,2},q),(1,{t}),(2,{t}),({ 1,2},{t}),(1,π),(2,π),({ 1,2},π)}

B×A={(q,1),(q,2),(q,{ 1,2}),({t},1),({t},2),({t},{ 1,2}),(π,1),(π,2),(π,{ 1,2})}

Explanation of Solution

Given:

A={1,2,{1,2}}

B={q,{t},π}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={1,2,{1,2}} and B={q,{t},π}

Then by definition of cross product,

A×B={(1,q),(2,q),({ 1,2},q),(1,{t}),(2,{t}),({ 1,2},{t}),(1,π),(2,π),({ 1,2},π)}

And

B×A={(q,1),(q,2),(q,{ 1,2}),({t},1),({t},2),({t},{ 1,2}),(π,1),(π,2),(π,{ 1,2})}

c.

To determine

To list: ordered pairs in A×B and B×A

c.

Expert Solution

Answer to Problem 13E

A×B={(∅,( ∅,{∅})),(∅,{∅}),(∅,( {∅},∅)),({∅},( ∅,{∅})),({∅},{∅}),({∅},( {∅},∅)),({ ∅,{∅}},( ∅,{∅})),({ ∅,{∅}},{∅}),({ ∅,{∅}},( {∅},∅))}

B×A={(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}})}

Explanation of Solution

Given:

A={∅,{∅},{∅,{∅}}}

B={(∅,{∅}),{∅},({∅},∅)}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={∅,{∅},{∅,{∅}}} and B={(∅,{∅}),{∅},({∅},∅)}

Then by definition of cross product,

A×B={(∅,( ∅,{∅})),(∅,{∅}),(∅,( {∅},∅)),({∅},( ∅,{∅})),({∅},{∅}),({∅},( {∅},∅)),({ ∅,{∅}},( ∅,{∅})),({ ∅,{∅}},{∅}),({ ∅,{∅}},( {∅},∅))}

And

B×A={(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}})}

d.

To determine

To list: ordered pairs in A×B and B×A

d.

Expert Solution

Answer to Problem 13E

A×B={((2,4),(4,1)),((3,1),(4,1)),((2,4),(2,3)),((3,1),(2,3))}

B×A={((4,1),(2,4)),((2,3),(2,4)),((4,1),(3,1)),((2,3),(3,1))}

Explanation of Solution

Given:

A={(2,4),(3,1)}

B={(4,1),(2,3)}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={(2,4),(3,1)} and B={(4,1),(2,3)}

Then by definition of cross product,

A×B={((2,4),(4,1)),((3,1),(4,1)),((2,4),(2,3)),((3,1),(2,3))}

And

B×A={((4,1),(2,4)),((2,3),(2,4)),((4,1),(3,1)),((2,3),(3,1))}

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Answer 3

Question

Chapter 2.2, Problem 13E

a.

To determine

To list:ordered pairs in A×B and B×A

a.

Expert Solution

Answer to Problem 13E

A×B={(1,a),(1,e),(1,k),(1,n),(1,r),(3,a),(3,e),(3,k),(3,n),(3,r),(5,a),(5,e),(5,k),(5,n),(5,r)}

B×A={(a,1),(e,1),(k,1),(n,1),(r,1),(a,3),(e,3),(k,3),(n,3),(r,3),(a,5),(e,5),(k,5),(n,5),(r,5)}

Explanation of Solution

Given:

A={1,3,5}

B={a,e,k,n,r}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={1,3,5} and B={a,e,k,n,r}

Then by definition of cross product,

A×B={(1,a),(1,e),(1,k),(1,n),(1,r),(3,a),(3,e),(3,k),(3,n),(3,r),(5,a),(5,e),(5,k),(5,n),(5,r)}

And

B×A={(a,1),(e,1),(k,1),(n,1),(r,1),(a,3),(e,3),(k,3),(n,3),(r,3),(a,5),(e,5),(k,5),(n,5),(r,5)}

b.

To determine

To list: ordered pairs in A×B and B×A

b.

Expert Solution

Answer to Problem 13E

A×B={(1,q),(2,q),({ 1,2},q),(1,{t}),(2,{t}),({ 1,2},{t}),(1,π),(2,π),({ 1,2},π)}

B×A={(q,1),(q,2),(q,{ 1,2}),({t},1),({t},2),({t},{ 1,2}),(π,1),(π,2),(π,{ 1,2})}

Explanation of Solution

Given:

A={1,2,{1,2}}

B={q,{t},π}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={1,2,{1,2}} and B={q,{t},π}

Then by definition of cross product,

A×B={(1,q),(2,q),({ 1,2},q),(1,{t}),(2,{t}),({ 1,2},{t}),(1,π),(2,π),({ 1,2},π)}

And

B×A={(q,1),(q,2),(q,{ 1,2}),({t},1),({t},2),({t},{ 1,2}),(π,1),(π,2),(π,{ 1,2})}

c.

To determine

To list: ordered pairs in A×B and B×A

c.

Expert Solution

Answer to Problem 13E

A×B={(∅,( ∅,{∅})),(∅,{∅}),(∅,( {∅},∅)),({∅},( ∅,{∅})),({∅},{∅}),({∅},( {∅},∅)),({ ∅,{∅}},( ∅,{∅})),({ ∅,{∅}},{∅}),({ ∅,{∅}},( {∅},∅))}

B×A={(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}})}

Explanation of Solution

Given:

A={∅,{∅},{∅,{∅}}}

B={(∅,{∅}),{∅},({∅},∅)}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={∅,{∅},{∅,{∅}}} and B={(∅,{∅}),{∅},({∅},∅)}

Then by definition of cross product,

A×B={(∅,( ∅,{∅})),(∅,{∅}),(∅,( {∅},∅)),({∅},( ∅,{∅})),({∅},{∅}),({∅},( {∅},∅)),({ ∅,{∅}},( ∅,{∅})),({ ∅,{∅}},{∅}),({ ∅,{∅}},( {∅},∅))}

And

B×A={(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}})}

d.

To determine

To list: ordered pairs in A×B and B×A

d.

Expert Solution

Answer to Problem 13E

A×B={((2,4),(4,1)),((3,1),(4,1)),((2,4),(2,3)),((3,1),(2,3))}

B×A={((4,1),(2,4)),((2,3),(2,4)),((4,1),(3,1)),((2,3),(3,1))}

Explanation of Solution

Given:

A={(2,4),(3,1)}

B={(4,1),(2,3)}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={(2,4),(3,1)} and B={(4,1),(2,3)}

Then by definition of cross product,

A×B={((2,4),(4,1)),((3,1),(4,1)),((2,4),(2,3)),((3,1),(2,3))}

And

B×A={((4,1),(2,4)),((2,3),(2,4)),((4,1),(3,1)),((2,3),(3,1))}

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Answer 4

Question

Chapter 2.2, Problem 13E

a.

To determine

To list:ordered pairs in A×B and B×A

a.

Expert Solution

Answer to Problem 13E

A×B={(1,a),(1,e),(1,k),(1,n),(1,r),(3,a),(3,e),(3,k),(3,n),(3,r),(5,a),(5,e),(5,k),(5,n),(5,r)}

B×A={(a,1),(e,1),(k,1),(n,1),(r,1),(a,3),(e,3),(k,3),(n,3),(r,3),(a,5),(e,5),(k,5),(n,5),(r,5)}

Explanation of Solution

Given:

A={1,3,5}

B={a,e,k,n,r}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={1,3,5} and B={a,e,k,n,r}

Then by definition of cross product,

A×B={(1,a),(1,e),(1,k),(1,n),(1,r),(3,a),(3,e),(3,k),(3,n),(3,r),(5,a),(5,e),(5,k),(5,n),(5,r)}

And

B×A={(a,1),(e,1),(k,1),(n,1),(r,1),(a,3),(e,3),(k,3),(n,3),(r,3),(a,5),(e,5),(k,5),(n,5),(r,5)}

b.

To determine

To list: ordered pairs in A×B and B×A

b.

Expert Solution

Answer to Problem 13E

A×B={(1,q),(2,q),({ 1,2},q),(1,{t}),(2,{t}),({ 1,2},{t}),(1,π),(2,π),({ 1,2},π)}

B×A={(q,1),(q,2),(q,{ 1,2}),({t},1),({t},2),({t},{ 1,2}),(π,1),(π,2),(π,{ 1,2})}

Explanation of Solution

Given:

A={1,2,{1,2}}

B={q,{t},π}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={1,2,{1,2}} and B={q,{t},π}

Then by definition of cross product,

A×B={(1,q),(2,q),({ 1,2},q),(1,{t}),(2,{t}),({ 1,2},{t}),(1,π),(2,π),({ 1,2},π)}

And

B×A={(q,1),(q,2),(q,{ 1,2}),({t},1),({t},2),({t},{ 1,2}),(π,1),(π,2),(π,{ 1,2})}

c.

To determine

To list: ordered pairs in A×B and B×A

c.

Expert Solution

Answer to Problem 13E

A×B={(∅,( ∅,{∅})),(∅,{∅}),(∅,( {∅},∅)),({∅},( ∅,{∅})),({∅},{∅}),({∅},( {∅},∅)),({ ∅,{∅}},( ∅,{∅})),({ ∅,{∅}},{∅}),({ ∅,{∅}},( {∅},∅))}

B×A={(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}})}

Explanation of Solution

Given:

A={∅,{∅},{∅,{∅}}}

B={(∅,{∅}),{∅},({∅},∅)}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={∅,{∅},{∅,{∅}}} and B={(∅,{∅}),{∅},({∅},∅)}

Then by definition of cross product,

A×B={(∅,( ∅,{∅})),(∅,{∅}),(∅,( {∅},∅)),({∅},( ∅,{∅})),({∅},{∅}),({∅},( {∅},∅)),({ ∅,{∅}},( ∅,{∅})),({ ∅,{∅}},{∅}),({ ∅,{∅}},( {∅},∅))}

And

B×A={(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}})}

d.

To determine

To list: ordered pairs in A×B and B×A

d.

Expert Solution

Answer to Problem 13E

A×B={((2,4),(4,1)),((3,1),(4,1)),((2,4),(2,3)),((3,1),(2,3))}

B×A={((4,1),(2,4)),((2,3),(2,4)),((4,1),(3,1)),((2,3),(3,1))}

Explanation of Solution

Given:

A={(2,4),(3,1)}

B={(4,1),(2,3)}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={(2,4),(3,1)} and B={(4,1),(2,3)}

Then by definition of cross product,

A×B={((2,4),(4,1)),((3,1),(4,1)),((2,4),(2,3)),((3,1),(2,3))}

And

B×A={((4,1),(2,4)),((2,3),(2,4)),((4,1),(3,1)),((2,3),(3,1))}

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Answer 5

Chapter 2.2, Problem 13E

a.

To determine

To list:ordered pairs in A×B and B×A

a.

Expert Solution

Answer to Problem 13E

A×B={(1,a),(1,e),(1,k),(1,n),(1,r),(3,a),(3,e),(3,k),(3,n),(3,r),(5,a),(5,e),(5,k),(5,n),(5,r)}

B×A={(a,1),(e,1),(k,1),(n,1),(r,1),(a,3),(e,3),(k,3),(n,3),(r,3),(a,5),(e,5),(k,5),(n,5),(r,5)}

Explanation of Solution

Given:

A={1,3,5}

B={a,e,k,n,r}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={1,3,5} and B={a,e,k,n,r}

Then by definition of cross product,

A×B={(1,a),(1,e),(1,k),(1,n),(1,r),(3,a),(3,e),(3,k),(3,n),(3,r),(5,a),(5,e),(5,k),(5,n),(5,r)}

And

B×A={(a,1),(e,1),(k,1),(n,1),(r,1),(a,3),(e,3),(k,3),(n,3),(r,3),(a,5),(e,5),(k,5),(n,5),(r,5)}

b.

To determine

To list: ordered pairs in A×B and B×A

b.

Expert Solution

Answer to Problem 13E

A×B={(1,q),(2,q),({ 1,2},q),(1,{t}),(2,{t}),({ 1,2},{t}),(1,π),(2,π),({ 1,2},π)}

B×A={(q,1),(q,2),(q,{ 1,2}),({t},1),({t},2),({t},{ 1,2}),(π,1),(π,2),(π,{ 1,2})}

Explanation of Solution

Given:

A={1,2,{1,2}}

B={q,{t},π}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={1,2,{1,2}} and B={q,{t},π}

Then by definition of cross product,

A×B={(1,q),(2,q),({ 1,2},q),(1,{t}),(2,{t}),({ 1,2},{t}),(1,π),(2,π),({ 1,2},π)}

And

B×A={(q,1),(q,2),(q,{ 1,2}),({t},1),({t},2),({t},{ 1,2}),(π,1),(π,2),(π,{ 1,2})}

c.

To determine

To list: ordered pairs in A×B and B×A

c.

Expert Solution

Answer to Problem 13E

A×B={(∅,( ∅,{∅})),(∅,{∅}),(∅,( {∅},∅)),({∅},( ∅,{∅})),({∅},{∅}),({∅},( {∅},∅)),({ ∅,{∅}},( ∅,{∅})),({ ∅,{∅}},{∅}),({ ∅,{∅}},( {∅},∅))}

B×A={(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}})}

Explanation of Solution

Given:

A={∅,{∅},{∅,{∅}}}

B={(∅,{∅}),{∅},({∅},∅)}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={∅,{∅},{∅,{∅}}} and B={(∅,{∅}),{∅},({∅},∅)}

Then by definition of cross product,

A×B={(∅,( ∅,{∅})),(∅,{∅}),(∅,( {∅},∅)),({∅},( ∅,{∅})),({∅},{∅}),({∅},( {∅},∅)),({ ∅,{∅}},( ∅,{∅})),({ ∅,{∅}},{∅}),({ ∅,{∅}},( {∅},∅))}

And

B×A={(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}})}

d.

To determine

To list: ordered pairs in A×B and B×A

d.

Expert Solution

Answer to Problem 13E

A×B={((2,4),(4,1)),((3,1),(4,1)),((2,4),(2,3)),((3,1),(2,3))}

B×A={((4,1),(2,4)),((2,3),(2,4)),((4,1),(3,1)),((2,3),(3,1))}

Explanation of Solution

Given:

A={(2,4),(3,1)}

B={(4,1),(2,3)}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={(2,4),(3,1)} and B={(4,1),(2,3)}

Then by definition of cross product,

A×B={((2,4),(4,1)),((3,1),(4,1)),((2,4),(2,3)),((3,1),(2,3))}

And

B×A={((4,1),(2,4)),((2,3),(2,4)),((4,1),(3,1)),((2,3),(3,1))}

Answer 6

Chapter 2.2, Problem 13E

a.

To determine

To list:ordered pairs in A×B and B×A

a.

Expert Solution

Answer to Problem 13E

A×B={(1,a),(1,e),(1,k),(1,n),(1,r),(3,a),(3,e),(3,k),(3,n),(3,r),(5,a),(5,e),(5,k),(5,n),(5,r)}

B×A={(a,1),(e,1),(k,1),(n,1),(r,1),(a,3),(e,3),(k,3),(n,3),(r,3),(a,5),(e,5),(k,5),(n,5),(r,5)}

Explanation of Solution

Given:

A={1,3,5}

B={a,e,k,n,r}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={1,3,5} and B={a,e,k,n,r}

Then by definition of cross product,

A×B={(1,a),(1,e),(1,k),(1,n),(1,r),(3,a),(3,e),(3,k),(3,n),(3,r),(5,a),(5,e),(5,k),(5,n),(5,r)}

And

B×A={(a,1),(e,1),(k,1),(n,1),(r,1),(a,3),(e,3),(k,3),(n,3),(r,3),(a,5),(e,5),(k,5),(n,5),(r,5)}

Answer 7

Chapter 2.2, Problem 13E

a.

To determine

To list:ordered pairs in A×B and B×A

Answer 8

a.

Expert Solution

Answer to Problem 13E

A×B={(1,a),(1,e),(1,k),(1,n),(1,r),(3,a),(3,e),(3,k),(3,n),(3,r),(5,a),(5,e),(5,k),(5,n),(5,r)}

B×A={(a,1),(e,1),(k,1),(n,1),(r,1),(a,3),(e,3),(k,3),(n,3),(r,3),(a,5),(e,5),(k,5),(n,5),(r,5)}

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given:

A={1,3,5}

B={a,e,k,n,r}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={1,3,5} and B={a,e,k,n,r}

Then by definition of cross product,

A×B={(1,a),(1,e),(1,k),(1,n),(1,r),(3,a),(3,e),(3,k),(3,n),(3,r),(5,a),(5,e),(5,k),(5,n),(5,r)}

And

B×A={(a,1),(e,1),(k,1),(n,1),(r,1),(a,3),(e,3),(k,3),(n,3),(r,3),(a,5),(e,5),(k,5),(n,5),(r,5)}

Answer 13

b.

To determine

To list: ordered pairs in A×B and B×A

b.

Expert Solution

Answer to Problem 13E

A×B={(1,q),(2,q),({ 1,2},q),(1,{t}),(2,{t}),({ 1,2},{t}),(1,π),(2,π),({ 1,2},π)}

B×A={(q,1),(q,2),(q,{ 1,2}),({t},1),({t},2),({t},{ 1,2}),(π,1),(π,2),(π,{ 1,2})}

Explanation of Solution

Given:

A={1,2,{1,2}}

B={q,{t},π}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={1,2,{1,2}} and B={q,{t},π}

Then by definition of cross product,

A×B={(1,q),(2,q),({ 1,2},q),(1,{t}),(2,{t}),({ 1,2},{t}),(1,π),(2,π),({ 1,2},π)}

And

B×A={(q,1),(q,2),(q,{ 1,2}),({t},1),({t},2),({t},{ 1,2}),(π,1),(π,2),(π,{ 1,2})}

Answer 14

b.

To determine

To list: ordered pairs in A×B and B×A

Answer 15

b.

Expert Solution

Answer to Problem 13E

A×B={(1,q),(2,q),({ 1,2},q),(1,{t}),(2,{t}),({ 1,2},{t}),(1,π),(2,π),({ 1,2},π)}

B×A={(q,1),(q,2),(q,{ 1,2}),({t},1),({t},2),({t},{ 1,2}),(π,1),(π,2),(π,{ 1,2})}

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given:

A={1,2,{1,2}}

B={q,{t},π}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={1,2,{1,2}} and B={q,{t},π}

Then by definition of cross product,

A×B={(1,q),(2,q),({ 1,2},q),(1,{t}),(2,{t}),({ 1,2},{t}),(1,π),(2,π),({ 1,2},π)}

And

B×A={(q,1),(q,2),(q,{ 1,2}),({t},1),({t},2),({t},{ 1,2}),(π,1),(π,2),(π,{ 1,2})}

Answer 20

c.

To determine

To list: ordered pairs in A×B and B×A

c.

Expert Solution

Answer to Problem 13E

A×B={(∅,( ∅,{∅})),(∅,{∅}),(∅,( {∅},∅)),({∅},( ∅,{∅})),({∅},{∅}),({∅},( {∅},∅)),({ ∅,{∅}},( ∅,{∅})),({ ∅,{∅}},{∅}),({ ∅,{∅}},( {∅},∅))}

B×A={(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}})}

Explanation of Solution

Given:

A={∅,{∅},{∅,{∅}}}

B={(∅,{∅}),{∅},({∅},∅)}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={∅,{∅},{∅,{∅}}} and B={(∅,{∅}),{∅},({∅},∅)}

Then by definition of cross product,

A×B={(∅,( ∅,{∅})),(∅,{∅}),(∅,( {∅},∅)),({∅},( ∅,{∅})),({∅},{∅}),({∅},( {∅},∅)),({ ∅,{∅}},( ∅,{∅})),({ ∅,{∅}},{∅}),({ ∅,{∅}},( {∅},∅))}

And

B×A={(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}})}

Answer 21

c.

To determine

To list: ordered pairs in A×B and B×A

Answer 22

c.

Expert Solution

Answer to Problem 13E

A×B={(∅,( ∅,{∅})),(∅,{∅}),(∅,( {∅},∅)),({∅},( ∅,{∅})),({∅},{∅}),({∅},( {∅},∅)),({ ∅,{∅}},( ∅,{∅})),({ ∅,{∅}},{∅}),({ ∅,{∅}},( {∅},∅))}

B×A={(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}})}

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given:

A={∅,{∅},{∅,{∅}}}

B={(∅,{∅}),{∅},({∅},∅)}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={∅,{∅},{∅,{∅}}} and B={(∅,{∅}),{∅},({∅},∅)}

Then by definition of cross product,

A×B={(∅,( ∅,{∅})),(∅,{∅}),(∅,( {∅},∅)),({∅},( ∅,{∅})),({∅},{∅}),({∅},( {∅},∅)),({ ∅,{∅}},( ∅,{∅})),({ ∅,{∅}},{∅}),({ ∅,{∅}},( {∅},∅))}

And

B×A={(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}}),(( ∅,{∅}),∅),({∅},{∅}),(( {∅},∅),{ ∅,{∅}})}

Answer 27

d.

To determine

To list: ordered pairs in A×B and B×A

d.

Expert Solution

Answer to Problem 13E

A×B={((2,4),(4,1)),((3,1),(4,1)),((2,4),(2,3)),((3,1),(2,3))}

B×A={((4,1),(2,4)),((2,3),(2,4)),((4,1),(3,1)),((2,3),(3,1))}

Explanation of Solution

Given:

A={(2,4),(3,1)}

B={(4,1),(2,3)}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={(2,4),(3,1)} and B={(4,1),(2,3)}

Then by definition of cross product,

A×B={((2,4),(4,1)),((3,1),(4,1)),((2,4),(2,3)),((3,1),(2,3))}

And

B×A={((4,1),(2,4)),((2,3),(2,4)),((4,1),(3,1)),((2,3),(3,1))}

Answer 28

d.

To determine

To list: ordered pairs in A×B and B×A

Answer 29

d.

Expert Solution

Answer to Problem 13E

A×B={((2,4),(4,1)),((3,1),(4,1)),((2,4),(2,3)),((3,1),(2,3))}

B×A={((4,1),(2,4)),((2,3),(2,4)),((4,1),(3,1)),((2,3),(3,1))}

Answer 30

d.

Expert Solution

Answer 31

d.

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

Given:

A={(2,4),(3,1)}

B={(4,1),(2,3)}

Definition Used:

Cross product of two sets A and B:

A×B={(a,b): a∈A and b∈B}

Given A={(2,4),(3,1)} and B={(4,1),(2,3)}

Then by definition of cross product,

A×B={((2,4),(4,1)),((3,1),(4,1)),((2,4),(2,3)),((3,1),(2,3))}

And

B×A={((4,1),(2,4)),((2,3),(2,4)),((4,1),(3,1)),((2,3),(3,1))}

Answer 34

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ordered pairs in A × B and B × A

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To list:ordered pairs in A×B and B×A

Answer to Problem 13E

Explanation of Solution

To list: ordered pairs in A×B and B×A

Answer to Problem 13E

Explanation of Solution

To list: ordered pairs in A×B and B×A

Answer to Problem 13E

Explanation of Solution

To list: ordered pairs in A×B and B×A

Answer to Problem 13E

Explanation of Solution

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