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00000CS 201121902

Suppose x is a real number. Consider the statement ^ 1052-4, then x=2”
Construct the converse, inverse, contrapositive of the given statement
Prove the following implication

Vx[P(x) > Q(x)], ഗം എല = Vx[RO)— -۲)۴([

Show that 79-२० ऽ is a valid inference from premises p—(qVr), १-२० 9, ‏وب‎ 7
Prove that n(n+2) is divisible by 4 by mathematical induction, if nis any even
positive integer.

Show that ഇ A (~qAr) ५ (qAr) ५ (pAr) = 1 using truth table.

Given the premises

P1: All men are selfish.

P2: All politicians are men.

Prove that the conclusion “All politicians are selfish” is a valid conclusion.
Show that ((p—q)A(q-r))—>(p—r) is a tautology.

Prove that 4z Q(z) is a valid conclusion from the premises

9100-0090], 3 PCy)

If the product of two integers a and b is even, then either a is even or b is even.
Prove the statement by contraposition.

Using proof by contradiction method, prove that “if 3n+2 is odd, then n is odd”

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