Questions: Given the conditional (a Longrightarrow b), what is the equivalent conditional? Select the correct answer below: (a Longrightarrow sim b) (sim b Longrightarrow sim a) (sim a Longrightarrow sim b) (b Longrightarrow a)

Given the conditional (a Longrightarrow b), what is the equivalent conditional?

Select the correct answer below:
(a Longrightarrow sim b)
(sim b Longrightarrow sim a)
(sim a Longrightarrow sim b)
(b Longrightarrow a)

Transcript text: Given the conditional $a \Longrightarrow b$, what is the equivalent conditional? Select the correct answer below: $a \Longrightarrow \sim b$ $\sim b \Longrightarrow \sim a$ $\sim a \Longrightarrow \sim b$ $b \Longrightarrow a$

Solution

Solution Steps

To determine if two conditional statements are equivalent, we need to identify the logical equivalence of the given conditional statement. The statement $ a \Longrightarrow b $ is logically equivalent to its contrapositive, which is $ \sim b \Longrightarrow \sim a $.

Step 1: Identify the Conditional Statement

The given conditional statement is $ a \Longrightarrow b $. This means that if $ a $ is true, then $ b $ must also be true.

Step 2: Determine the Equivalent Conditional

To find the equivalent conditional, we need to identify its contrapositive. The contrapositive of $ a \Longrightarrow b $ is $ \sim b \Longrightarrow \sim a $. This means that if $ b $ is false, then $ a $ must also be false.

Step 3: Evaluate the Options

We are given several options to choose from: