JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Mathematical Reasoning *

The number of ordered triplets of the truth values of

p, q

and

r

such that the truth value of the statement

(p \lor q) \land (p \lor r) \Rightarrow (q \lor r)

is True, is equal to

Answer: 7

Solution

Construct a truth table for all 8 combinations of truth values for

p, q, r

. The statement

(p \lor q) \land (p \lor r) \Rightarrow (q \lor r)

is false only when the antecedent is true and the consequent is false. Checking all cases: the statement is false only for

(T, F, F)

. Thus it is true for 7 out of 8 cases.

JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Integer answer