Question

6. Write the converse of the following true conditional statement. If the converse is false, write a counterexample:

If a < 10, then a < 15.

(1 point)

If a > 10, then a > 15; false
counterexample: a = 12 and a <15

If a < 15, then a < 10; false
counterexample: a = 12 and a > 10

If a<15, then a<10; true

If a> 15, then a > 10; true

Answer 1

its a just took this reasoning and proof unit test

Explanation:

Answer 2

False; counterexample a = 12

Explanation:

The statement If a < 10, then a < 15 is a true statement because any number to the left of 10 on the number line (representing a number smaller than 10), are for sure to the left of 15 (thus representing a number smaller than 15). But its converse:

If a<15 then a<10 is a false statement. A clear counterexample is a=12, which is smaller than 15, but it is not smaller than 12.