Question

Select the contrapositive of the conditional statement:
“If lines are perpendicular, then they meet to form right angles.”
A. If lines are not perpendicular, then they do not meet to form right angles.
B. If lines meet to form right angles, then the lines are perpendicular
C. If lines do not meet to form right angles, then the lines are not perpendicular.
D. Lines are perpendicular if and only if they meet to form right angles

Answer 1

hi jason. are you familiar with negation?

Answer 2

Not particularly. I've heard the word but i'm unclear on it all.

Answer 3

ok then. i am gonna walk you through this.

Answer 4

so when you have a conditional statement, If P, then Q, the contrapositive is If not Q, then not P.

Answer 5

does that make sense?

Answer 6

Yes.

Answer 7

now if P is 'lines are perpendicular' and Q is 'they meet to form right angles, what is not P and not Q?

Answer 8

it is ok here if you dont know.

Answer 9

A?

Answer 10

sorry no. so the contrapositive reverses the conditional statement and negates both parts. This means that not P=the lines are not perpendicular and not Q=they do not meet to form right angles.

Answer 11

so you are going to get If not Q, then not P. try that. if you cannot see it, i will finish it for u.

Answer 12

I would guess C, but this is difficult for me!

Answer 13

C is the correct answer!!

Answer 14

i also know it is difficult, and not just for you, but for me, for many others. I just have some experience on you. :)

Answer 15

it will get easier. :)

Answer 16

notice how i consider P to be the part after IF and before THEN and Q is the part after THEN

Answer 17

they are called the hypothesis and the conclusion, respectively

Answer 18

so, for the contrapositive, you negate both P and Q and then switch their places. ok?

Answer 19

Okay!

Answer 20

anything else i can help with Jason?

Answer 21

Actually, yes!
If p-> q is a true statement, then which other statement is also true?

Would q -> work?

Answer 22

My mistake, q -> p

Answer 23

for p-> q, q->p is the converse. unless a statement is biconditional (if and only if), then the converse is not the same as the original statement. however, the contrapositive of p->q is ~p->~q and it IS the same.

Answer 24

wait!

Answer 25

the contrapositive of p->q is ~q->~p. really sorry there.

Answer 26

so a conditional statement and its contrapositive are the same. ok?

Answer 27

It's all good!

Answer 28

just so long as you have the jist of it. any questions?

Answer 29

I think i'm good for now. You more than deserve the a "best responce!" Thanks!

Answer 30

thanks. you have a nice evening. take care. :)