JEE PYQ: Mathematical Reasoning Question 1
Question 1 - 2021 (16 Mar Shift 1)
Which of the following Boolean expression is a tautology?
(1) $(p \wedge q) \vee (p \vee q)$
(2) $(p \wedge q) \vee (p \to q)$
(3) $(p \wedge q) \wedge (p \to q)$
(4) $(p \wedge q) \to (p \to q)$
Type: MCQ
Show Answer
Answer: (4)
Solution
$(p \wedge q) \to (p \to q)$ is tautology.
Option (1): $(p \wedge q) \vee (p \vee q)$ — Not a tautology.
Option (2): $(p \wedge q) \vee (p \to q) = (p \wedge q) \vee (\sim p \vee q) = \sim p \vee q$ — Not a tautology.
Option (3): $(p \wedge q) \wedge (p \to q) = (p \wedge q) \wedge (\sim p \vee q) = p \wedge q$ — Not a tautology.
Option (4): $(p \wedge q) \to (p \to q) = \sim(p \wedge q) \vee (\sim p \vee q) = (\sim p \vee \sim q) \vee (\sim p \vee q) = \sim p \vee (\sim q \vee q) = \sim p \vee t = t$ (tautology)
BETA
