This chapter is currently out of syllabus
1
JEE Main 2023 (Online) 13th April Morning Shift
+4
-1
Out of Syllabus

The negation of the statement $$((A \wedge(B \vee C)) \Rightarrow(A \vee B)) \Rightarrow A$$ is

A
equivalent to $$B ~\vee \sim C$$
B
equivalent to $$\sim A$$
C
equivalent to $$\sim C$$
D
a fallacy
2
JEE Main 2023 (Online) 12th April Morning Shift
+4
-1
Out of Syllabus

Among the two statements

$$(\mathrm{S} 1):(p \Rightarrow q) \wedge(p \wedge(\sim q))$$ is a contradiction and

$$(\mathrm{S} 2):(p \wedge q) \vee((\sim p) \wedge q) \vee(p \wedge(\sim q)) \vee((\sim p) \wedge(\sim q))$$ is a tautology

A
both are false.
B
only (S1) is true.
C
both are true.
D
only (S2) is true.
3
JEE Main 2023 (Online) 11th April Evening Shift
+4
-1
Out of Syllabus

The converse of $$((\sim p) \wedge q) \Rightarrow r$$ is

A
$$((\sim p) \vee q) \Rightarrow r$$
B
$$(\sim \mathrm{r}) \Rightarrow \mathrm{p} \wedge \mathrm{q}$$
C
$$(\mathrm{p} \vee(\sim \mathrm{q})) \Rightarrow(\sim \mathrm{r})$$
D
$$(\sim \mathrm{r}) \Rightarrow((\sim \mathrm{p}) \wedge \mathrm{q})$$
4
JEE Main 2023 (Online) 10th April Evening Shift
+4
-1
Out of Syllabus

The statement $$\sim[p \vee(\sim(p \wedge q))]$$ is equivalent to :

A
$$(\sim(p \wedge q)) \wedge q$$
B
$$\sim(p \vee q)$$
C
$$(p \wedge q) \wedge(\sim p)$$
D
$$\sim(p \wedge q)$$
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