## Related questions with answers

Let's consider the conditional statement "If it is raining, then it is cloudy" to be a true statement. a In your own words, explain how the converse statement is different from the conditional statement. b In your own words, explain how the contrapositive statement is equivalent to the conditional statement. c If we switched the hypothesis and conclusion of "All squares have four right angles" as a conditional statement, would the statement be true or false? Explain.

Solution

Verified$\textbf{(a)}$

Identify the hypothesis and conclusion of the given conditional $(A\to B)$:

$\begin{align*} &\textbf{Hypothesis $(A)$: }\text{It is raining.}\\ &\textbf{Conclusion $(B)$: }\text{It is cloudy.}\\ \end{align*}$

The $\textbf{\color{#4257b2}converse}$ is the statement formed by exchanging the hypothesis and conclusion of a conditional. In symbols, $B\to A$.

If it is cloudy, then it is raining. The converse is different from the conditional because it is $\text{\textcolor{#c34632}{false}}$ as it may be snowing when it is cloudy.

## Create a free account to view solutions

## Create a free account to view solutions

## Recommended textbook solutions

#### Geometry: Common Core, New York Edition

1st Edition•ISBN: 9780789189318 (1 more)Joyce Bernstein#### Big Ideas Math Geometry: A Common Core Curriculum

1st Edition•ISBN: 9781608408399 (1 more)Boswell, Larson## More related questions

1/4

1/7