Problem 1. (a) Let A = {1,2} and let B = {3,4, 5}. Describe all functions from A to B. (You could draw arrow diagrams, or give a list of relations.) (b) In general, if A is a set with a elements and B is a set with b elements, how many func- tions are there from A to B? Give your answer as a formula in terms of a and b and ex- plain your answer. (c) How many of the functions from the last part are injections? Again, give your answer as a formula in terms of a and b and explain it.

Q: 3. Simplify the following. Be sure to state all restrictions on equality. x²-1 (a) 2x²-2x-4 (c)…

A: x2-12x2-2x-4 x2-169-x·x2+x-90x2+14x+40

Q: 11. -6 -4 -2 0 2 4 6

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Q: You are given a real number N. How should you write it as a sum of two real numbers so that their…

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Q: Set B (x+7)(x-3) 20 20 x+6 x+7 <0 x-5 x+3 20 x-10 1. x-1 x+3 3. 2.

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Q: A ball is tossed into the air, 3 metres above ground. The height, h metres, t seconds after being =…

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Q: If 'I' denotes the 'divides' relation, then what can be said about 'b' if (2 | b) ^ (b | 2) (2…

A: there are two relations 2 is divisible by b and b is divisible by 2 and there is a disjunction(means…

Q: Define the relation R = {(a.b): a + b < ab} = A x B with A = {1,2,4} and B = {2,5,6). List all the…

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Q: Describe in words an example of a binary relation on A. Your example should be a single concise…

A: If set A has n elements than number of relation on A is 2n.n.

Q: Below are four sets of ordered pairs. Identify each using the following: n = the set of ordered…

A: Given that n = the set of ordered pairs does not represent a functionf = the set of ordered pairs…

Q: Let A = {1,2,3,4} and B = {4,5,6,7,8} and R be the definite relation of A to B determined by the…

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Q: . The relation ⋆ means “this number written out in English has this many letters”. For example, 6 ⋆…

A: A relation R  on a set A is said to (1) Reflexive : forall x in A implies (x,x) in R . (2)…

Q: [4,9] how would I express this as an inequality involving x? I thought I know i thought it would be…

A: [4,9] how would I express this as an inequality involving x

Q: 2. Let A:= {1,2, 3, 4} =: B and T:= {(a, b) E A x B | l e Z}. (a) Find A x B. (b) Find T (c) Check…

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Q: Find the Domain of 1, if f(=) 0(s-6) %3D O Domain: y is all real numbers O Domain: y N0 O Domain: NO…

A: Given f(x)=6(x-6)2 To find f-1, assume y=f(x) then swap variables to find f-1

Q: C. Use the table to evaluate cach expression: 2 3 4 3 5 4 f(x) g(x) 4 2 3 3 a) f(g(0)) b) g(g(1)) c)…

A: Recall: f∘g(x)=f(g(x)) f±gx=f(x)±g(x) f.g(x) = f(x).g(x) Note : According to Bartleby guidelines,…

Q: 4. Make a table of values for each relation. Use the table to determine if the relation is…

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Q: The algebraic translation of "x is at most 7" is

A: Given : The algebraic translation of " x is at most 7" is ______________ .

Q: Let A = {1, 2} and B = {3, 4}. Find the number of relations from A to B.

A: Number of elements in A=2 ...................................In B=2

Q: Given the sets: A = {21, 31, 51, 81, 91} and B= {31, 41, 61, 71, 91} and the relation R = {(x, y) /…

A: The given sets are A = {21, 31, 51, 81, 91} and B= {31, 41, 61, 71, 91}. The relation is R=x, y| x,…

Q: 5. Determine the domains of each of the following functions. State your answers in set-builder…

A: To find the domain

Q: On the set of real numbers x2 + y2 = 1 Function. If x is a real number and y is an integer number:…

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Q: Please solve the remaining part. From number 4 to 6. Thank you.

A: Since you have posted multiple questions, we will provide the solution only to the first question as…