Question

Classify the following conditional as true or false.

If $r>t$and $s>t$, then $r>s$.

Short answer

The statement is false.

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:

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

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

Therefore, the statement is false.