(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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Class 11

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Mathematical Reasoning

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Mathematical logic

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For each of the following compound statements,first identify the connecting words and then break it into component statements.The sand heats up quickly in the Sun and does not cool down fast at night.

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For each of the following compound statements,first identify the connecting words and then break it into component statements.
The sand heats up quickly in the Sun and does not cool down fast at night.

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There is no rain without clouds.

Are the following pairs of statements negations of each other:
$1$. The number $x$ is a rational number.
$2$. The number $x$ is an irrational number.

Are the following pairs of statements negations of each other:
$1$. The number $x$ is not a rational number.
$2$. The number $x$ is not an irrational number.