JEE Main 2020 — Mathematical Reasoning Question with Solution
From: JEE Main 2020 (Online) 8th January Morning Slot
Question
Which one of the following is a tautology?
Choose an option
Show full solutionCorrect option: D
Correct answer
D(P (P Q)) Q
Step-by-step explanation
Option A :
Option B :
Option C :
Q (P (P Q))
~ Q (P (P Q))
~ Q (P (~P Q))
~ Q (P ~P) (P Q))
~ Q (ƒ (P Q))
~ Q (P Q)
(~Q P) (~Q Q)
(~ Q P) t
~ Q P
Option D :
(P (P Q)) Q
(P (~P Q)) Q
((P ~P) (P Q)) Q
(ƒ (P Q)) Q
P Q Q
~ (P Q) Q
(~ P) (~Q) Q
(~ P) t
t
| P | Q | P Q | P (P Q) |
|---|---|---|---|
| T | T | T | T |
| T | F | T | T |
| F | T | T | F |
| F | F | F | F |
Option B :
| P | Q | P Q | P (P Q) |
|---|---|---|---|
| T | T | T | T |
| T | F | F | T |
| F | T | F | F |
| F | F | F | F |
Option C :
Q (P (P Q))
~ Q (P (P Q))
~ Q (P (~P Q))
~ Q (P ~P) (P Q))
~ Q (ƒ (P Q))
~ Q (P Q)
(~Q P) (~Q Q)
(~ Q P) t
~ Q P
Option D :
(P (P Q)) Q
(P (~P Q)) Q
((P ~P) (P Q)) Q
(ƒ (P Q)) Q
P Q Q
~ (P Q) Q
(~ P) (~Q) Q
(~ P) t
t
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