Whether the function f ( n , m ) = 2 n + 3 m ; f : N × N → N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

Question

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Answer 1

Question

Chapter 3.1, Problem 22E

a)

To determine

Whether the function f(n,m)=2n+3m;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

b)

To determine

Whether the function f(n,m)=2n+3m;f:Z×Z→Z is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

c)

To determine

Whether the function f(n,m)=14n+22m;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

d)

To determine

Whether the function f(n,m)=89n+246m;f:Z×Z→Z is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

e)

To determine

Whether the function f(n,m)=n2+m2+1;f:Z×Z→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

f)

To determine

Whether the function f(n,m)=⌊nm⌋+1;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

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Answer 2

Question

Chapter 3.1, Problem 22E

a)

To determine

Whether the function f(n,m)=2n+3m;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

b)

To determine

Whether the function f(n,m)=2n+3m;f:Z×Z→Z is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

c)

To determine

Whether the function f(n,m)=14n+22m;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

d)

To determine

Whether the function f(n,m)=89n+246m;f:Z×Z→Z is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

e)

To determine

Whether the function f(n,m)=n2+m2+1;f:Z×Z→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

f)

To determine

Whether the function f(n,m)=⌊nm⌋+1;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

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Answer 3

Question

Chapter 3.1, Problem 22E

a)

To determine

Whether the function f(n,m)=2n+3m;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

b)

To determine

Whether the function f(n,m)=2n+3m;f:Z×Z→Z is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

c)

To determine

Whether the function f(n,m)=14n+22m;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

d)

To determine

Whether the function f(n,m)=89n+246m;f:Z×Z→Z is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

e)

To determine

Whether the function f(n,m)=n2+m2+1;f:Z×Z→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

f)

To determine

Whether the function f(n,m)=⌊nm⌋+1;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

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See solution

Answer 4

Question

Chapter 3.1, Problem 22E

a)

To determine

Whether the function f(n,m)=2n+3m;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

b)

To determine

Whether the function f(n,m)=2n+3m;f:Z×Z→Z is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

c)

To determine

Whether the function f(n,m)=14n+22m;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

d)

To determine

Whether the function f(n,m)=89n+246m;f:Z×Z→Z is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

e)

To determine

Whether the function f(n,m)=n2+m2+1;f:Z×Z→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

f)

To determine

Whether the function f(n,m)=⌊nm⌋+1;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

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Answer 5

Chapter 3.1, Problem 22E

a)

To determine

Whether the function f(n,m)=2n+3m;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

b)

To determine

Whether the function f(n,m)=2n+3m;f:Z×Z→Z is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

c)

To determine

Whether the function f(n,m)=14n+22m;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

d)

To determine

Whether the function f(n,m)=89n+246m;f:Z×Z→Z is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

e)

To determine

Whether the function f(n,m)=n2+m2+1;f:Z×Z→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

f)

To determine

Whether the function f(n,m)=⌊nm⌋+1;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

Answer 6

Chapter 3.1, Problem 22E

a)

To determine

Whether the function f(n,m)=2n+3m;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

Answer 7

Chapter 3.1, Problem 22E

a)

To determine

Whether the function f(n,m)=2n+3m;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

Answer 8

b)

To determine

Whether the function f(n,m)=2n+3m;f:Z×Z→Z is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

Answer 9

b)

To determine

Whether the function f(n,m)=2n+3m;f:Z×Z→Z is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

Answer 10

c)

To determine

Whether the function f(n,m)=14n+22m;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

Answer 11

c)

To determine

Whether the function f(n,m)=14n+22m;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

Answer 12

d)

To determine

Whether the function f(n,m)=89n+246m;f:Z×Z→Z is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

Answer 13

d)

To determine

Whether the function f(n,m)=89n+246m;f:Z×Z→Z is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

Answer 14

e)

To determine

Whether the function f(n,m)=n2+m2+1;f:Z×Z→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

Answer 15

e)

To determine

Whether the function f(n,m)=n2+m2+1;f:Z×Z→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

Answer 16

f)

To determine

Whether the function f(n,m)=⌊nm⌋+1;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

Answer 17

f)

To determine

Whether the function f(n,m)=⌊nm⌋+1;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

Answer 18

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Answer 19

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Answer 20

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Answer 21

Ch. 3.1 - True/False Questions A function from a set A to a...Ch. 3.1 - Prob. 2TFQ Ch. 3.1 - Prob. 3TFQ Ch. 3.1 - Prob. 4TFQ Ch. 3.1 - Prob. 5TFQ Ch. 3.1 - True/False Questions Define f:ZZ by f(x)=x+2. Then...Ch. 3.1 - Prob. 7TFQ Ch. 3.1 - Prob. 8TFQ Ch. 3.1 - Prob. 9TFQ Ch. 3.1 - Prob. 10TFQ

Whether the function f ( n , m ) = 2 n + 3 m ; f : N × N → N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

Solution Summary: The author explains that f is not one-to-one as some values in range have more than one pre-image.

Whether the function f(n,m)=2n+3m;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

Whether the function f(n,m)=2n+3m;f:Z×Z→Z is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

Whether the function f(n,m)=14n+22m;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

Whether the function f(n,m)=89n+246m;f:Z×Z→Z is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

Whether the function f(n,m)=n2+m2+1;f:Z×Z→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

Whether the function f(n,m)=⌊nm⌋+1;f:N×N→N is one-to-one and/or onto. Also give a proof or exhibit a counterexample to justify the answer.

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Chapter 3 Solutions