The logical statement -p-q- - -q - p- is equivalent to

Explanation of the correct option.Compute the equivalent statement.pqp⇒qpq⇒ p(p⇒q)∧(q⇒ p)TTTFFFTFFFTFFTTTTTFFTTTTFrom the table it can be seen that (p⇒q)∧(q⇒ p) ...

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Standard X

Mathematics

Basic Proportionality Theorem

The logical s...

Question

The logical statement $(p \Rightarrow q) \land (q \Rightarrow ~ p)$ is equivalent to

$~ p$

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$p$

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$q$

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$~ q$

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Solution

The correct option is A
$~ p$

Explanation of the correct option.
Compute the equivalent statement.
$p$
$q$
$p \Rightarrow q$
$~ p$
$q \Rightarrow ~ p$
$(p \Rightarrow q) \land (q \Rightarrow ~ p)$
$T$
$T$
$T$
$F$
$F$
$F$
$T$
$F$
$F$
$F$
$T$
$F$
$F$
$T$
$T$
$T$
$T$
$T$
$F$
$F$
$T$
$T$
$T$
$T$
From the table it can be seen that $(p \Rightarrow q) \land (q \Rightarrow ~ p)$ is equivalent to $~ p$ .
Hence option $(A)$ is the correct option.

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$p$	$q$	$p \Rightarrow q$	$~ p$	$q \Rightarrow ~ p$	$(p \Rightarrow q) \land (q \Rightarrow ~ p)$
$T$	$T$	$T$	$F$	$F$	$F$
$T$	$F$	$F$	$F$	$T$	$F$
$F$	$T$	$T$	$T$	$T$	$T$
$F$	$F$	$T$	$T$	$T$	$T$

The logical statement p⇒q∧q⇒~p is equivalent to

The correct option is A ~pExplanation of the correct option.Compute the equivalent statement.pqp⇒q~pq⇒~pp⇒q∧q⇒~pTTTFFFTFFFTFFTTTTTFFTTTTFrom the table it can be seen that p⇒q∧q⇒~p is equivalent to ~p.Hence option A is the correct option.

The logical statement $(p \Rightarrow q) \land (q \Rightarrow ~ p)$ is equivalent to