1
MHT CET 2025 21st April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The logical statement

$$ [\sim(\sim p \vee q) \vee(p \wedge r) \wedge(\sim q \wedge r)] $$

is equivalent to

A
$(\mathrm{p} \wedge \mathrm{r}) \wedge \sim \mathrm{q}$
B
$(\sim p \wedge \sim q) \wedge r$
C
$\sim p \vee r$
D
$\quad(p \wedge \sim q) \vee r$
2
MHT CET 2025 21st April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the statement pattern $(p \wedge q) \rightarrow(r \vee \sim s)$ is false, then the truth values of $p, q, r$ and $s$ are respectively

A
$T, F, T, F$
B
$T, T, T, F$
C
$T, T, F, F$
D
$T, T, F, T$
3
MHT CET 2025 20th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

The negation of $(p \wedge \sim q) \rightarrow(p \vee \sim q)$ is

A
a tautology
B
a contingency
C
a contradiction
D
equivalent to $\mathrm{p} \wedge \mathrm{q}$
4
MHT CET 2025 20th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equivalent statement of "If three vertices of a triangle are represented by cube roots of unity, then the triangle is an equilateral triangle" is

A

Three vertices of a triangle are represented by cube roots of unity and the triangle is not an equilateral triangle.

B
If a triangle is an equilateral triangle then the three vertices of a triangle are represented by cube roots of unity.
C
If three vertices of triangle are not represented by cube roots of unity then the triangle is not an equilateral triangle.
D
If a triangle is not an equilateral triangle then the three vertices of the triangle can not be represented by cube roots of unity.
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