Question

Example 2 Identify the hypothesis and conclusion of each statement.

Then write each statement in if-then form.

The sum of two even numbers is an even number.

Short answer

"Sum of two even numbers" is a hypothesis and "is an even number" is a conclusion.

"if two even numbers are added, their sum is always an even number".

Step-by-step solution

Step 1. Given Statement.

The sum of two even numbers is an even number.

Step 2. Even numbers.

Even numbers are the numbers that are divisible by 2, i.e. can be written as 2x, where x is any number.

Step 3. Description of step.

To identify the hypothesis and conclusion in the given statement

Since the addition of two even numbers say 2p and 2 q is

2p+2q = 2(p + q) is also an even number.

Then the "sum of two even numbers" is a hypothesis and “is an even number" is a conclusion/result.

And it is written in an if-then form as:

Thus, if the two even numbers are added, their sum is always an even number.