The statement (sim( p Leftrightarrow sim q )) | vedclass

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(C) We are given the expression $(\sim( p \Leftrightarrow \sim q )) \wedge q$.First,recall that $\sim( p \Leftrightarrow \sim q )$ is equivalent to $p

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equivalent to $( p \Rightarrow q ) \wedge q$

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(C) We are given the expression $(\sim( p \Leftrightarrow \sim q )) \wedge q$.First,recall that $\sim( p \Leftrightarrow \sim q )$ is equivalent to $p \Leftrightarrow q$ because $\sim( p \Leftrightarrow \sim q ) \equiv p \Leftrightarrow \sim(\sim q) \equiv p \Leftrightarrow q$.Now,the expression becomes $( p \Leftrightarrow q ) \wedge q$.We know that $p \Leftrightarrow q$ is $( p$ $\Rightarrow q ) \wedge ( q$ $\Rightarrow p )$.So,$( p \Leftrightarrow q ) \wedge q \equiv ( p$ $\Rightarrow q ) \wedge ( q$ $\Rightarrow p ) \wedge q$.Since $( q \Rightarrow p ) \wedge q \equiv q \wedge p$,the expression simplifies to $( p \Rightarrow q ) \wedge ( p \wedge q ) \equiv p \wedge q$.Alternatively,checking the truth table for $( p \Leftrightarrow q ) \wedge q$:If $p=T, q=T$,then $(T \Leftrightarrow T) \wedge T = T \wedge T = T$.If $p=F, q=T$,then $(F \Leftrightarrow T) \wedge T = F \wedge T = F$.If $p=T, q=F$,then $(T \Leftrightarrow F) \wedge F = F \wedge F = F$.If $p=F, q=F$,then $(F \Leftrightarrow F) \wedge F = T \wedge F = F$.Comparing this with option $(C)$: $( p \Rightarrow q ) \wedge q$.If $p=T, q=T$,then $(T \Rightarrow T) \wedge T = T \wedge T = T$.If $p=F, q=T$,then $(F \Rightarrow T) \wedge T = T \wedge T = T$.This does not match.Wait,let's re-evaluate the original expression: $(\sim( p \Leftrightarrow \sim q )) \wedge q$.Since $\sim( p \Leftrightarrow \sim q ) \equiv p \Leftrightarrow q$,the expression is $( p \Leftrightarrow q ) \wedge q$.This is equivalent to $p \wedge q$.Looking at the options,none of the provided options are $p \wedge q$. Let us re-check the logic.Actually,$( p \Rightarrow q ) \wedge q$ is equivalent to $q \wedge p$ if $p$ is true,but generally $( p \Rightarrow q ) \wedge q \equiv q \wedge p$ is not true. Wait,$( p \Rightarrow q ) \wedge q \equiv (\sim p \vee q) \wedge q \equiv q$.Let's re-examine the expression: $(\sim( p \Leftrightarrow \sim q )) \wedge q \equiv (p \Leftrightarrow q) \wedge q$. This is $p \wedge q$.Given the options,there might be a typo in the question or options. However,based on standard logic,$(p \Leftrightarrow q) \wedge q \equiv p \wedge q$.

The statement $(\sim( p \Leftrightarrow \sim q )) \wedge q$ is :

Similar Questions

For each of the following compound statements,first identify the corresponding component statements. Then check whether the statements are true or not.
If a triangle $ABC$ is equilateral,then it is isosceles.

Which of the following statement patterns is a tautology?
$S_{1} \equiv \sim p \rightarrow (q \leftrightarrow p)$
$S_{2} \equiv \sim p \vee \sim q$
$S_{3} \equiv (p$ $\rightarrow q) \wedge (q$ $\rightarrow p)$
$S_{4} \equiv (q \rightarrow p) \vee (\sim p \leftrightarrow q)$

Consider the following three statements:
$P: 5$ is a prime number.
$Q: 7$ is a factor of $192$.
$R: \text{L.C.M. of } 5 \text{ and } 7 \text{ is } 35$.
Then,the truth value of which one of the following statements is true?

Consider the following statements:
Statement $1$: If a quadrilateral is a square,then all of its sides are equal.
Statement $2$: If all the sides of a quadrilateral are equal,then it is a square.

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The statement $(\sim( p \Leftrightarrow \sim q )) \wedge q$ is :

Similar Questions

For each of the following compound statements,first identify the corresponding component statements. Then check whether the statements are true or not.If a triangle $ABC$ is equilateral,then it is isosceles.

Which of the following statement patterns is a tautology?$S_{1} \equiv \sim p \rightarrow (q \leftrightarrow p)$$S_{2} \equiv \sim p \vee \sim q$$S_{3} \equiv (p$ $\rightarrow q) \wedge (q$ $\rightarrow p)$$S_{4} \equiv (q \rightarrow p) \vee (\sim p \leftrightarrow q)$

Consider the following three statements:$P: 5$ is a prime number.$Q: 7$ is a factor of $192$.$R: \text{L.C.M. of } 5 \text{ and } 7 \text{ is } 35$.Then,the truth value of which one of the following statements is true?

Consider the following statements:Statement $1$: If a quadrilateral is a square,then all of its sides are equal.Statement $2$: If all the sides of a quadrilateral are equal,then it is a square.