This chapter is currently out of syllabus
1
JEE Main 2023 (Online) 31st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
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
2
JEE Main 2023 (Online) 31st January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus

$$(\mathrm{S} 1)~(p \Rightarrow q) \vee(p \wedge(\sim q))$$ is a tautology

$$(\mathrm{S} 2)~((\sim p) \Rightarrow(\sim q)) \wedge((\sim p) \vee q)$$ is a contradiction.

Then

A
only (S2) is correct
B
both (S1) and (S2) are correct
C
only (S1) is correct
D
both (S1) and (S2) are wrong
3
JEE Main 2023 (Online) 30th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus

Consider the following statements:

P : I have fever

Q: I will not take medicine

$\mathrm{R}$ : I will take rest.

The statement "If I have fever, then I will take medicine and I will take rest" is equivalent to :

A
$((\sim P) \vee \sim Q) \wedge((\sim P) \vee \sim R)$
B
$(P \vee \sim Q) \wedge(P \vee \sim R)$
C
$((\sim P) \vee \sim Q) \wedge((\sim P) \vee R)$
D
$(P \vee Q) \wedge((\sim P) \vee R)$
4
JEE Main 2023 (Online) 30th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus

Among the statements :

$$(\mathrm{S} 1)~((\mathrm{p} \vee \mathrm{q}) \Rightarrow \mathrm{r}) \Leftrightarrow(\mathrm{p} \Rightarrow \mathrm{r})$$

$$(\mathrm{S} 2)~((\mathrm{p} \vee \mathrm{q}) \Rightarrow \mathrm{r}) \Leftrightarrow((\mathrm{p} \Rightarrow \mathrm{r}) \vee(\mathrm{q} \Rightarrow \mathrm{r}))$$

A
only (S1) is a tautology
B
neither (S1) nor (S2) is a tautology
C
both (S1) and (S2) are tautologies
D
only (S2) is a tautology
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