Chapter 6: Q3. (page 218)

Classify the following conditional as true or false.
If $r > t$ and $s > t$ , then $r > s$ .

Short Answer

Expert verified

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.

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Classify the following conditional as true or false.
If $r > t$ and $s > t$ , then $r > s$ .

Short Answer

Step by step solution

Step 1. Apply the concept of conditional statement.

Step 2. Step description.

Step 3. Step description.

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Classify the following conditional as true or false.If r>tand s>t, then r>s.

Short Answer

Step by step solution

Step 1. Apply the concept of conditional statement.

Step 2. Step description.

Step 3. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Geometry

Theoretical and Mathematical Physics

Calculus

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Classify the following conditional as true or false.
If $r > t$ and $s > t$ , then $r > s$ .