1) Answer the following questions. Explain your reasoning:

a) Without using the truth table, show that the following statement is a tautology: [3

marks]

(((R → S) → R) → R)

b) Without using the truth table, show that the following statement is true: [3 marks]

((PAQ) → (PVQ)) = (P→ Q)

c) Negate the following statement: [3 marks]

Vx:P(x) ^ [3x: (Q(x) ^ R(x)]

d) For the following statement, write down a logically equivalent statement which contains

no operators other than and →: [3 marks]

7

PA -Q V R