(A) Let the given propositions be $C_1, C_2, \dots, C_9$. We test the truth values for $p, q, r, s$ to maximize the number of true propositions.If we

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(A) Let the given propositions be $C_1, C_2, \dots, C_9$. We test the truth values for $p, q, r, s$ to maximize the number of true propositions.If we assign $p=F, q=F, r=T, s=F$:$C_1: F \vee T \vee F = T$$C_2: F \vee F \vee T = T$$C_3: F \vee T \vee F = T$$C_4: T \vee F \vee F = T$$C_5: T \vee F \vee T = T$$C_6: T \vee F \vee T = T$$C_7: F \vee T \vee T = T$$C_8: F \vee F \vee T = T$$C_9: T \vee T \vee T = T$All $9$ propositions are true for this assignment.

Class 11 Mathematics Mathematical Reasoning Mathematical logic

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The maximum number of compound propositions,out of $p \vee r \vee s$,$p \vee \sim r \vee \sim s$,$p \vee \sim q \vee s$,$\sim p \vee \sim r \vee s$,$\sim p \vee \sim r \vee \sim s$,$\sim p \vee q \vee \sim s$,$q \vee r \vee \sim s$,$q \vee \sim r \vee \sim s$,$\sim p \vee \sim q \vee \sim s$ that can be made simultaneously true by an assignment of the truth values to $p, q, r$ and $s$,is equal to

JEE MAIN 2022 All JEE MAIN

A
$9$
B
$6$
C
$4$
D
$3$

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Mathematical Reasoning

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

MediumMHT CET 2025

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Given the statement: "If a quadrilateral is a parallelogram,then its diagonals bisect each other."
Identify the following statements as the contrapositive or converse of the given statement:
$(i)$ If the diagonals of a quadrilateral do not bisect each other,then the quadrilateral is not a parallelogram.
$(ii)$ If the diagonals of a quadrilateral bisect each other,then it is a parallelogram.

Easy

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Consider the following statements:
Statement $I$: If a quadrilateral $ABCD$ is a square,then all of its sides are equal.
Statement $II$: If all the sides of a quadrilateral $ABCD$ are equal,then $ABCD$ is a square.
Then:

EasyMHT CET 2022

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Which of the following is not a statement?

Easy

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

MediumJEE MAIN 2014

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

Consider the following statements:Statement $I$: If a quadrilateral $ABCD$ is a square,then all of its sides are equal.Statement $II$: If all the sides of a quadrilateral $ABCD$ are equal,then $ABCD$ is a square.Then:

Which of the following is not a statement?

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

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Consider the following statements:
Statement $I$: If a quadrilateral $ABCD$ is a square,then all of its sides are equal.
Statement $II$: If all the sides of a quadrilateral $ABCD$ are equal,then $ABCD$ is a square.
Then: