Problem 2 - Algebra 1: Concepts and Skills

Question

State the hypothesis and the conclusion of the statement "If \(x\) is an even number, then \(x^{2}\) is an even number."

Step-by-Step Solution

Answer

The hypothesis is 'If \(x\) is an even number' and the conclusion is 'then \(x^{2}\) is an even number.'

Step 1: Identifying the Hypothesis

In an 'If...then...' statement, the 'if' part is always the hypothesis. So, in the statement 'If \(x\) is an even number, then \(x^{2}\) is an even number.', the hypothesis is that '\(x\) is an even number.'.

Step 2: Identifying the Conclusion

The 'then' part of an 'If...then...' statement is the conclusion. Therefore, in the same statement, the conclusion is that '\(x^{2}\) is an even number.'.

Step 3: Statement of Hypothesis and Conclusion

Putting the parts together, we can state that the hypothesis is '\(x\) is an even number' and the conclusion is '\(x^{2}\) is an even number.'.