Answer the following questions. Explain your reasoning:
a) Without using the truth table, prove if the following statement is tautology
or not.
((r→q) ⋁ ((q∧r)→q)) ∧ (r→(s→r))
[2 marks]
b) Without using the truth table, show that the following statements are true:
i.
P(q v r) ≡ (p ∧ ¬ q)  r
ii.
(¬p → q) ∨ (r → q) ≡ r → (p ∨ q)
c) Rewrite each sentence symbolically:
i.
ii.
The product of any two real numbers x and y is negative.
There are real numbers x and y such that x+3= 4y.
[4 marks]
[2 marks]
[2 marks]
d) For the following statement, write down a logically equivalent statement
which contains no operators other than ¬ and ∧:
�
� ∨(→)