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Determine which of the statement are true and which are
Chapter 4, Problem 18E(choose chapter or problem)
Determine which of the statements in 15–20 are true and which are false. Prove each true statement directly from the definitions, and give a counterexample for each false statement. In case the statement is false, determine whether a small change would make it true. If so, make the change and prove the new statement. Follow the directions for writing proofs on page 154.
If r and s are any two rational numbers, then \(\frac{r+s}{2}\) is rational.
Text Transcription:
r+s/2
Questions & Answers
QUESTION:
Determine which of the statements in 15–20 are true and which are false. Prove each true statement directly from the definitions, and give a counterexample for each false statement. In case the statement is false, determine whether a small change would make it true. If so, make the change and prove the new statement. Follow the directions for writing proofs on page 154.
If r and s are any two rational numbers, then \(\frac{r+s}{2}\) is rational.
Text Transcription:
r+s/2
ANSWER:Solution:
Step 1:
In this problem, we need to show that if r and s are any two rational numbers, then is rational.