1
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
The statement pattern $[(p \rightarrow q) \wedge \sim q] \rightarrow r$ is a tautology when $r$ is equivalent to
A
$\mathrm{p} \wedge \sim \mathrm{q}$
B
$q \vee p$
C
$p \wedge q$
D
$\sim q$
2
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

Consider the three statements

$\mathrm{p}: \forall \mathrm{n} \in \mathbb{N}, 10 \mathrm{n}-3$ is a prime number, when n is not divisible by 3.

$\mathrm{q}: \frac{2}{\sqrt{3}}, \frac{-2}{\sqrt{3}}, \frac{-1}{\sqrt{3}}$ are the direction cosines of a directed line.

$\mathrm{r}: \sin x$ is an increasing function in the interval $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$.

Then which of the following statement pattern has truth value true?

A
$\quad(p \wedge q) \leftrightarrow r$
B
$(p \rightarrow q) \rightarrow \sim r$
C
$(\sim p \vee q) \wedge r$
D
$\quad(\sim p \wedge \sim q) \leftrightarrow \sim r$
3
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Truth values of $\mathrm{p} \rightarrow \mathrm{r}$ is F and $\mathrm{p} \leftrightarrow \mathrm{q}$ is F . Then the truth values of $(\sim p \vee q) \rightarrow(p \vee \sim q)$ and $(p \wedge \sim q) \rightarrow(\sim p \wedge q)$ are respectively

A
$\mathrm{T, F}$
B
$\mathrm{F}, \mathrm{T}$
C
$\mathrm{T}, \mathrm{T}$
D
$\mathrm{F, F}$
4
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The statement $\sim(p \leftrightarrow \sim q)$ is

A
equivalent to $\mathrm{p} \leftrightarrow \mathrm{q}$
B
a fallacy
C
a tautology
D
equivalent to $\sim \mathrm{p} \leftrightarrow \mathrm{q}$
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