# Bijections, Denumerability, Tautologies, Sets, Logic and Proofs (7 Problems)

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Consider the compound statement (P ^ Q) V (~ P ^ R)

a) Find the truth table for the statement.

b) IS the statement a tautology?

c) In the following program code, what has to be the output for the answr to be "yes"?

...

2. Given the following sets A = {1.2,3.4}, B = {2,3,4,5}, and C= {2,4,6}

a) Find ....

4. Prove that if ... are bijections....then...is a bijection...

5. Prove that the set of Gausian integers is denumerable.

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Bijections, Denumerability, Tautologies, Sets, Logic and Proofs are investigated. The solution is detailed and well presented.

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1. (a) 0-False, 1-True

p q r p.q ~p.r p.q+~p.r

0 0 0 0 0 0

0 0 1 0 1 1

0 1 0 0 0 0

0 1 1 0 1 1

1 0 0 0 0 0

1 0 1 0 0 0

1 1 0 1 0 1

1 1 1 1 0 1

(b) No. (p q) (~p r) is not Tautology as its value is not True always.

(c) This block of program prints 'yes' when P is False and R is True

2. A={1, 2, 3, 4}, B={2, 3, 4, 5} and C={2, 4, 6}

A B={1, 2, 3, 4, 5}, A B={2, 3, 4}, ...

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