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Expert-verified Found in: Page 218 ### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279 # Classify the following conditional as true or false.If $r>t$ and $s>t$, then $r>s$.

The statement is false.

See the step by step solution

## Step 1. Apply the concept of conditional statement.

Conditional statements are those statements where a hypothesis is followed by a conclusion. It is also known as an " If-then" statement.

## Step 2. Step description.

Consider the statement “if $r>t$ and $s>t$, then $r>s$.”

An inequality opens on the greater side.

Here $r>t$ implies that r is greater than t and $s>t$ implies that s is greater than t.

Consider $r=3,t=2,s=4$.

## Step 3. Step description.

Now, check the conditional statement by $r=3,t=2,s=4$ as follows:

$\begin{array}{l}r>t,s>t⇒r>s\\ 3>2,4>2⇒3>4\end{array}$

Which is impossible such that 3 is not greater than 4.

Therefore, the statement is false. ### Want to see more solutions like these? 