Answer: The proofs are given below.
Step-by-step explanation: We are given to prove that the following statements are tautologies using truth table :
(a) ¬r ∨ (¬r → p) b. ¬(p → q) → ¬q
We know that a statement is a TAUTOLOGY is its value is always TRUE.
(a) The truth table is as follows :
r p ¬r ¬r→p ¬r ∨ (¬r → p)
T T F T T
T F F T T
F T T T T
F F T F T
So, the statement (a) is a tautology.
(b) The truth table is as follows :
p q ¬q p→q ¬(p→q) ¬(p→q)→q
T T F T F T
T F T F T T
F T F T F T
F F T T F T
So, the statement (B) is a tautology.
Hence proved.
