Question

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

@mathmale

Answer 2

First identify the hypothesis (p) and the conclusion (q).

Answer 3

okay 20 is the hypothesis is 20 and the conclusion is 30

Answer 4

Correct :) Now we need to switch these two places....the conclusion would go where the hypothesis is and the hypothesis would go where the conclusion is...

`If q, then p`

How would it be written?

Answer 5

if x< 30 then x<20?

Answer 6

Nice!

Answer 7

so the answer would be A?

Answer 8

That depends if the converse is true....is it true?

Answer 9

I think so.

Answer 10

Well if we have `x<30` then we can choose a number that can be less than 30...lets try `25`....now it says that since its less than 30 then its `less than 20` so is 25 less than 20?

Answer 11

No it's not less then twenty

Answer 12

Correct so the converse is false.

Answer 13

So it would be c?

Answer 14

Not C it would be B. Due to the fact that the converse is `if x< 30 then x<20`

Answer 15

Oh okay, thank you, could you help with another one?