This chapter is currently out of syllabus
1
JEE Main 2023 (Online) 31st January Morning Shift
+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
2
JEE Main 2023 (Online) 30th January Evening Shift
+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
$(P \vee Q) \wedge((\sim P) \vee R)$
3
JEE Main 2023 (Online) 30th January Morning Shift
+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
4
JEE Main 2023 (Online) 29th January Morning Shift
+4
-1
Out of Syllabus

If $$p,q$$ and $$r$$ are three propositions, then which of the following combination of truth values of $$p,q$$ and $$r$$ makes the logical expression $$\left\{ {(p \vee q) \wedge \left( {( \sim p) \vee r} \right)} \right\} \to \left( {( \sim q) \vee r} \right)$$ false?

A
$$p = F,q = T,r = F$$
B
$$p = T,q = T,r = F$$
C
$$p = T,q = F,r = T$$
D
$$p = T,q = F,r = F$$
EXAM MAP
Medical
NEET