Question

Check my answers please.

Instructions, write the if-then form, hypothesis, conclusion, converse, inverse, and contrapositive for the following statement:

Two angles are complementary if the sum of their measures is 90(degrees).

Answer 1

Sheesh am I wrong that badly? You've been typing for awhile :o

Answer 2

I'm thinking from a logic perspective that the hypothesis should be " sum of their measures is 90(degrees" and the consequent should be "Two angles are complementary" - http://en.wikipedia.org/wiki/Hypothesis

If we let P = "sum of their measures is 90(degrees)"
let Q = "Two angles are complementary"

Then If P then Q is the structure we are dealing with.

Next we find the relationships between conditional statements: Converse, Inverse and Contrapositive - http://en.wikipedia.org/wiki/Contrapositive

Converse: if Q then P
Inverse: If Not P then Not Q
Contrapositive: If Not Q then Not P

Answer 3

@ybarrap

Answer 4

perfect!

Answer 5

Also do I leave the if then form as is?

Answer 6

I think so, just check the hypothesis and consequent (conclusion?) part.

Answer 7

Just to clarify the the hypothesis should be " sum of their measures is 90(degrees"

and the conclusion should be "sum of their measures is 90(degrees" and the consequent should be "Two angles are complementary, or were those just examples?

Answer 8

I just reread I think my original two go well with what you corrected?

Answer 9

I think we agreed on all 3!

Answer 10

maybe not the last (contrapositive)

Answer 11

Okay, swell! I hate to bother you for any more help but this is a two part question and it then asks to tell wheter the converse, inverse and contrapositive is T or F, I don't understand what true or false means in this context?

Answer 12

I have to circle T or F, I don't understand because if they were false would that not make them wrong?

Answer 13

Yes, based on the definition of complimentary angles, some forms would make them false. BTW, If P then Q is true then so it's contrapositive --- they are logically equivalent.

http://en.wikipedia.org/wiki/Complementary_angles#Combine_angle_pairs

If the converse is true (which it is), then so is the contrapostive of the converse. In our case, the contrapositive of the converse is the inverse!

So all are True!

Answer 14

Well I appreciate all of your help, thank you so much!

Answer 15

NP - you are a good student. Keep it up!