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1
JEE Main 2023 (Online) 6th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Statement $$\mathrm{(P \Rightarrow Q) \wedge(R \Rightarrow Q)}$$ is logically equivalent to :

A
$$(P \Rightarrow R) \wedge(Q \Rightarrow R)$$
B
$$(P \Rightarrow R) \vee(Q \Rightarrow R)$$
C
$$(P \wedge R) \Rightarrow Q$$
D
$$(P \vee R) \Rightarrow Q$$
2
JEE Main 2023 (Online) 1st February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Which of the following statements is a tautology?

A
$$\mathrm{p\vee(p\wedge q)}$$
B
$$(\mathrm{p\wedge(p\to q))\to\,\sim q}$$
C
$$\mathrm{p\to (p\wedge (p\to q))}$$
D
$$(\mathrm{p\wedge q)\to(\sim (p)\to q)}$$
3
JEE Main 2023 (Online) 1st February Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

The negation of the expression $$q \vee \left( {( \sim \,q) \wedge p} \right)$$ is equivalent to

A
$$( \sim \,p) \wedge ( \sim \,q)$$
B
$$( \sim \,p) \vee q$$
C
$$p \wedge ( \sim \,q)$$
D
$$( \sim \,p) \vee ( \sim \,q)$$
4
JEE Main 2023 (Online) 31st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
The number of values of $\mathrm{r} \in\{\mathrm{p}, \mathrm{q}, \sim \mathrm{p}, \sim \mathrm{q}\}$ for which $((\mathrm{p} \wedge \mathrm{q}) \Rightarrow(\mathrm{r} \vee \mathrm{q})) \wedge((\mathrm{p} \wedge \mathrm{r}) \Rightarrow \mathrm{q})$ is a tautology, is :
A
2
B
1
C
4
D
3
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