Given below are two statements:
$p: 25 \text{ is a multiple of } 5.$
$q: 25 \text{ is a multiple of } 8.$
Write the compound statements connecting these two statements with "And" and "Or". In both cases,check the validity of the compound statement.
$p: 25 \text{ is a multiple of } 5.$
$q: 25 \text{ is a multiple of } 8.$
Write the compound statements connecting these two statements with "And" and "Or". In both cases,check the validity of the compound statement.
(N/A) The compound statement with 'And' is: "$25$ is a multiple of $5$ and $8$."
This is a false statement,since $25$ is not a multiple of $8$.
The compound statement with 'Or' is: "$25$ is a multiple of $5$ or $8$."
This is a true statement,since $25$ is a multiple of $5$ (even though it is not a multiple of $8$,the 'Or' condition is satisfied if at least one statement is true).
This is a false statement,since $25$ is not a multiple of $8$.
The compound statement with 'Or' is: "$25$ is a multiple of $5$ or $8$."
This is a true statement,since $25$ is a multiple of $5$ (even though it is not a multiple of $8$,the 'Or' condition is satisfied if at least one statement is true).
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Similar Questions
Consider the statement patterns:
$A. (q \to p) \lor (p \to q)$
$B. (\sim p \lor \sim q) \leftrightarrow \sim (p \land q)$
$C. [(p \lor q) \land \sim p] \land \sim q$
$D. (p \land q) \land (\sim p \lor \sim q)$
Then identify the nature of these statement patterns.
$A. (q \to p) \lor (p \to q)$
$B. (\sim p \lor \sim q) \leftrightarrow \sim (p \land q)$
$C. [(p \lor q) \land \sim p] \land \sim q$
$D. (p \land q) \land (\sim p \lor \sim q)$
Then identify the nature of these statement patterns.
DifficultMHT CET 2026
View Solution$p \Rightarrow q$ can also be written as
Easy
View SolutionWhich of the following statements is correct?
$(a)$ $S_1: (p \wedge q) \equiv \sim(p \rightarrow \sim q)$
$(b)$ $S_2: (p \wedge q) \wedge (\sim p \vee \sim q)$ is a tautology
$(c)$ $S_3: [p \wedge (p$ $\rightarrow \sim q)]$ $\rightarrow q$ is a contradiction
$(d)$ $S_4: p$ $\rightarrow (q$ $\rightarrow p)$ is a contingency
$(a)$ $S_1: (p \wedge q) \equiv \sim(p \rightarrow \sim q)$
$(b)$ $S_2: (p \wedge q) \wedge (\sim p \vee \sim q)$ is a tautology
$(c)$ $S_3: [p \wedge (p$ $\rightarrow \sim q)]$ $\rightarrow q$ is a contradiction
$(d)$ $S_4: p$ $\rightarrow (q$ $\rightarrow p)$ is a contingency
If $p$: Every square is a rectangle and $q$: Every rhombus is a kite,then the truth values of $p \rightarrow q$ and $p \leftrightarrow q$ are $ . . . . . . $ and $ . . . . . . $ respectively.
The statement $p \to (p \leftrightarrow q)$ is logically equivalent to :-
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