Question

Which of the following propositions is tautology?
a. (p v q)→q b. p v (q→p) c. p v (p→q) d. Both (b) & (c)

Answer 1

Step-by-step explanation:

a) ~(pvq)vq = ~p ^ ~q v q= ~p ^T = ~p

b) p v (q->p) = p v ~qv p= p v ~q

c) p v (p->q)= pv ~p v q = Tv q = T

c is tautology as it is T, true in all cases

Answer 2

The correct answer is option (d.) Both (b) & (c).

Explanation:

• (p v q)→q and p v (p→q) propositions is tautology.
• In mathematical logic, a tautology is referred as a formula or assertion that is true in every possible interpretation.
• For example: "x=y or x≠y".
• Similarly, "either the ball can be green, or the ball can not be green" is always true, regardless of the colour of the ball.
• From the truth table, we can conclude that the truth values of (p v q)→q and p v (p→q) are always true.
• Hence, (p v q)→q and p v (p→q) are tautology.