### Home > CAAC > Chapter 6 > Lesson 6.3.1 > Problem 6-109

Identify the hypothesis and conclusion for each of the following statements. Then decide if the statement is sometimes true, always true, or never true.

**Justify**your decision.*ab*is odd if*a*and*b*are prime numbers.If

*a*and*b*are negative real numbers, then*a*+*b*is positive.

Write the hypothesis and conclusion.

Hypothesis: *a* and *b* are prime numbers

Conclusion: *ab* is odd

Try using a few examples to test your hypothesis and conclusion.

(2)(7) = ?

(3)(11) = ?

(5)(13) = ?

Sometimes true because 2 is a prime number.

Write the hypothesis and conclusion.

*a* and *b* are negative real numbers *a* + *b* is positive

Try using a few examples to test your hypothesis and conclusion.

−1 + −3 = ?

−7 + −2 = ?

−11 + −4 = ?

Never true because the set of negative real numbers is closed under addition. Closed means that if you start with 2 negatives and add them you get another negative.