If the truth value of the Boolean expression $$\left( {\left( {p \vee q} \right) \wedge \left( {q \to r} \right) \wedge \left( { \sim r} \right)} \right) \to \left( {p \wedge q} \right)$$ is false, then the truth values of the statements p, q, r respectively can be :
A
T F T
B
F F T
C
T F F
D
F T F
Explanation
p
q
r
$$\underbrace {p \vee q}_a$$
$$\underbrace {q \to r}_b$$
$${a \wedge b}$$
$${ \sim r}$$
$$\underbrace {a \wedge b \wedge ( \sim r)}_c$$
$$\underbrace {p \wedge q}_d$$
$$c \to d$$
T
F
T
T
T
T
F
F
F
T
F
F
T
F
T
F
F
F
F
T
T
F
F
T
T
T
T
T
F
F
F
T
F
T
F
F
T
F
F
T
4
JEE Main 2021 (Online) 27th July Morning Shift
MCQ (Single Correct Answer)
The compound statement $$(P \vee Q) \wedge ( \sim P) \Rightarrow Q$$ is equivalent to :
A
$$P \vee Q$$
B
$$P \wedge \sim Q$$
C
$$ \sim (P \Rightarrow Q)$$
D
$$ \sim (P \Rightarrow Q) \Leftrightarrow P \wedge \sim Q$$
Explanation
Using Truth Table :
Questions Asked from Mathematical Reasoning
On those following papers in MCQ (Single Correct Answer)
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