The Boolean expression $ (\sim(p \land q)) \lor q $ is equivalent to:

Question

Let $f(x)=|\log_e x|-|x-1|+5$. Statement 1: $f(x)$ is differentiable for all $x\in(0,\infty)$
Statement 2: $f(x)$ is increasing in $(1,\infty)$
Statement 3: $f(x)$ is decreasing in $(0,1)$
Which of the following is correct?

Answer 1

The provided logical expression is: \[ (\sim(p \land q)) \lor q. \] Step 1: Simplify the expression. Using Boolean algebra, we get: \[ \sim(p \land q) = \sim p \lor \sim q. \] The expression then transforms to: \[ (\sim p \lor \sim q) \lor q = \sim p \lor q. \] Step 2: Rewrite in implication form. Given that: \[ \sim p \lor q = p \to (p \lor q), \] the simplified expression is equivalent to $ p \to (p \lor q) $. Consequently, the correct answer is $ \boxed{(4)} $.

The Boolean expression \( (\sim(p \land q)) \lor q \) is equivalent to:

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The Correct Option is D

Solution and Explanation

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