Question

Which answer is the contrapositive of the conditional statement, and correctly shows if the conditional statement is the contrapositive are true or false?

Answer 1

@Vocaloid

Answer 2

Conditional: If p, then q.
Converse: If q, then p.
Inverse: If not p, then not q.
Contrapositive: If not q, then not p.

Answer 3

Start with your given conditional.
Look above at how to arrive at the contrapositive.
What is the contrapositive of your original conditional?

Answer 4

Conditional: \(\sf If~ \color{red}{p}, ~then ~\color{green}{q}.\)
Conditional: \(\sf If~\) \(\color{red}{5x \ne 30}\)\(\sf, ~then ~\)\(\color{green}{x \ne 6}\).

Answer 5

if 5x does not =30, then x does not =6

Answer 6

For the contrapositive you do two things:
1. Negate the hypothesis and the conclusion.
2. Switch the hypothesis and the conclusion.

Answer 7

You have the conditional that you just wrote.
Now negate the hypothesis and negate the conclusion.
The original hypothesis is: \(5x \ne 30\).
How do you negate that?

Answer 8

i got the anwser... i got if x=6, then 5x=30. the conditional and contrapositive are both true

Answer 9

Correct.

Answer 10

Thanks for all the help @Vocaloid @mathstudent55 ... i got all 44/44 correct

Answer 11

Contrapositive: \(\sf If~\)\(\color{green}{not~q}\)\(\sf,~then ~\)\(\color{red}{not~p}\).

Contrapositive: \(\sf If~\)\(\color{green}{x = 6}\)\(\sf,~then ~\)\(\color{red}{5x = 30}\).

Answer 12

You're welcome.
Congrats on your high grade!