Question:
The logical statement $[\sim (\sim p \vee q) \vee (p \wedge r) \wedge (\sim q \wedge r)]$ is equivalent to:
The logical statement $[\sim (\sim p \vee q) \vee (p \wedge r) \wedge (\sim q \wedge r)]$ is equivalent to:
Updated On: Apr 28, 2025
- $(p \wedge r) \wedge \sim q$
- $(\sim p \wedge \sim q) \wedge r $
- $\sim p \vee r$
- $(p \wedge \sim q) \vee r$
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The Correct Option is A
Solution and Explanation
$s [\sim (\sim p \vee q) \wedge (p \wedge r )] \cap ( \sim q \wedge r)$
$\equiv [(p \wedge \sim q) \vee ( p \wedge r)] \wedge (\sim q \wedge r)$
$\equiv [ p \wedge (\sim q \vee r)] \wedge ( \sim q \wedge r )$
$ \equiv \; p \wedge (\sim q \wedge r )$
$\equiv (p \wedge r) \sim q$
$\equiv [(p \wedge \sim q) \vee ( p \wedge r)] \wedge (\sim q \wedge r)$
$\equiv [ p \wedge (\sim q \vee r)] \wedge ( \sim q \wedge r )$
$ \equiv \; p \wedge (\sim q \wedge r )$
$\equiv (p \wedge r) \sim q$
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Mathematical Reasoning
Mathematical reasoning or the principle of mathematical reasoning is a part of mathematics where we decide the truth values of the given statements. These reasoning statements are common in most competitive exams like JEE and the questions are extremely easy and fun to solve.
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Mathematically, reasoning can be of two major types such as:
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