Question

WILL MEDAL
10.Write the converse of the following true conditional statement. If the converse is false, write a counterexample.
If x<20, then x<30.
A. If x<30, then x<20; true
B.If x<30, then x<20; false
Counterexample: x=27 and x>27 .
C. If x>20, then x>30; false
Counterexample: x=25 and x<30
D. If x>30, then x>20; true

Answer 1

The converse is when you switch the hypothesis and conclusion of a statement, for example:

An cat is an animal
Converse: An animal is a cat
But notice that just because it's the converse, it doesn't mean it's true, not all animals are cats. So what is the converse of:

If x<20, then x<30?? And once you find the converse, is it true?

Answer 2

Ummm, I would say A?

Answer 3

Actually no, in between A & B right now xD

Answer 4

Im*

Answer 5

The converse is A, but if x<30, then x<20 is not necessarily true, I can think of some numbers that are less that 30, but not less than 20 (21-29). So what do you think the answer is? It has to have a counterexample if the converse is false.

Answer 6

So it would be B ?

Answer 7

Correct

Answer 8

Thank you so much! I really appreciate it (:

Answer 9

But I think there is a typo, it should be x=25, and x>20

Answer 10

There's still C but I don't think that would be correct xD

Answer 11

It makes sense, but I don't think you change the inequality signs with converse because it would not be A and B from the original statement.