This chapter is currently out of syllabus
1
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
$$p = T,q = F,r = F$$
2
JEE Main 2023 (Online) 25th January Evening Shift
+4
-1
Out of Syllabus

Let $$\Delta ,\nabla \in \{ \wedge , \vee \}$$ be such that $$\mathrm{(p \to q)\Delta (p\nabla q)}$$ is a tautology. Then

A
$$\Delta = \vee ,\nabla = \vee$$
B
$$\Delta = \vee ,\nabla = \wedge$$
C
$$\Delta = \wedge ,\nabla = \wedge$$
D
$$\Delta = \wedge ,\nabla = \vee$$
3
JEE Main 2023 (Online) 25th January Morning Shift
+4
-1
Out of Syllabus

The statement $$\left( {p \wedge \left( { \sim q} \right)} \right) \Rightarrow \left( {p \Rightarrow \left( { \sim q} \right)} \right)$$ is

A
a tautology
B
equivalent to $$\left( { \sim p} \right) \vee \left( { \sim q} \right)$$
C
D
$$p \vee q$$
4
JEE Main 2023 (Online) 24th January Evening Shift
+4
-1
Out of Syllabus

Let p and q be two statements. Then $$\sim \left( {p \wedge (p \Rightarrow \, \sim q)} \right)$$ is equivalent to

A
$$\left( { \sim p} \right) \vee q$$
B
$$p \vee \left( {p \wedge ( \sim q)} \right)$$
C
$$p \vee \left( {p \wedge q} \right)$$
D
$$p \vee \left( {\left( { \sim p} \right) \wedge q} \right)$$
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