1
JEE Main 2023 (Online) 30th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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
2
JEE Main 2023 (Online) 29th January Morning Shift
MCQ (Single Correct Answer)
+4
-1

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
$$p = T,q = F,r = F$$
3
JEE Main 2023 (Online) 25th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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
$$\Delta = \wedge ,\nabla = \vee $$
4
JEE Main 2023 (Online) 25th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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
a contradiction
D
$$p \vee q$$
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