“If the alternate exterior angles are congruent, then the lines are parallel.”

What is the inverse of the statement?

If the lines are parallel, then the alternate exterior angles are congruent.

If the alternate exterior angles are congruent, then the lines should be parallel.

If the alternate exterior angles are not congruent, then the lines are not parallel.

If the lines are not parallel, then the alternate exterior angles are not congruent.

Question

“If the alternate exterior angles are congruent, then the lines are parallel.” 
  
What is the inverse of the statement?

 If the lines are parallel, then the alternate exterior angles are congruent.

 If the alternate exterior angles are congruent, then the lines should be parallel.

 If the alternate exterior angles are not congruent, then the lines are not parallel.

 If the lines are not parallel, then the alternate exterior angles are not congruent.

parthkohli · Answer

Just put the 'not's.

parthkohli · Answer

just to give you an example:
if it is a cat, then it is an animal.

the inverse would be:
if it is not a cat, then it is not an animal

parthkohli · Answer

The last one is the contrapositive, not the inverse.

parthkohli · Answer

If a statement is true, then its inverse is ALWAYS false.

anonymous · Answer

ok, now im really confused.

parthkohli · Answer

Statement: If P then Q.
Inverse: If not P then not Q.

parthkohli · Answer

Compare this with the question

anonymous · Answer

so its the first choice?

parthkohli · Answer

Does it have the 'not's?

parthkohli · Answer

The given statement is a positive statement, so its inverse would be negative, that is, that it will have the 'not's.

anonymous · Answer

no, but the word "inverse" means reversed in position, order, direction, or tendency

parthkohli · Answer

"Inverse" here is the logical inverse.

anonymous · Answer

ok so if its not the last choice and it should include the 'not's then the only choice left is the 3rd. correct? since it is talking about the "logical inverse" instead of the order being switched. correct?

parthkohli · Answer

Yeah, correct. When it switches and has the 'not's, then we have the contrapositive instead of the inverse.

parthkohli · Answer

So yeah, it is 3rd.

anonymous · Answer

alright thanks :)

parthkohli · Answer

I gave you a medal because you wanted to understand :)))

parthkohli · Answer

I really have to bounce now, see ya

anonymous · Answer

bye

jhonyy9 · Answer

excuz me but i think that the first one is invers of this statement 

my opinion

anonymous · Answer

thats what i hald thought given the meaning to 'inverse' something

anonymous · Answer

*had

jhonyy9 · Answer

ParthKohli sorry but i think that what you have explned with your words is negation of this statement and not the inverse

jhonyy9 · Answer

explaned -sorry

jhonyy9 · Answer

LivforMusic how do you think ?

jhonyy9 · Answer

so one example 

let the statement 

if i am boy so result that i am not girl 

than the invers of this will be 

if i am girl so result that i am not a boy

right ?

kinggeorge · Answer

@ParthKohli is correct. 

Statement: If P then Q.
Inverse: If not P then not Q.

What jhonny wrote is called the converse.

anonymous · Answer

ok thank you @KingGeorge

kinggeorge · Answer

I think I should mention however, that both the inverse and the converse are logically equivalent.

jhonyy9 · Answer

thank you very much KingGeorge for your explication 

good luck

bye

jhonyy9 · Answer

so than how it is exactly now right the inverse and the converse are logically equivalent ???

jhonyy9 · Answer

inverse equal converse ???

kinggeorge · Answer

Since we know $$P\implies Q \Longleftrightarrow \neg Q\implies \neg\, P$$we can just as easily say $$\neg\, P \implies \neg Q \Longleftrightarrow Q\implies P$$The statements are logically equivalent, but not the same.

kinggeorge · Answer

@LivForMusic Here's a handy chart that may help with similar problems. 

Statement: $P\implies Q$
Contrapositive: $\neg\,Q\implies \neg\, P$
Inverse: $\neg\,P\implies\neg\,Q$
Converse: $Q\implies P$

jhonyy9 · Answer

thank you KingGeorge 

so LivforMusic i understand - i think - what have wrote there KingGeorge - so but i think that my opinion from this your exersice and the right ansvere remain what i have wrote firstly so that the first option will be right 

sorry for this complication in this case

jhonyy9 · Answer

what is the inverse of this statement ?

 If the lines are parallel, then the alternate exterior angles are congruent.

this was my question and the answer what i have got is:

jhonyy9 · Answer

there might be two interpretations,
 
1. if angles are congruent, then line are parallel.. 
2. lines r not parallel, than angles r not congruent... 

this was the first answer on this my question 


so after this how do you think how is your exercise solved right ?

jhonyy9 · Answer

KingGeorge can you tell me please what is your opinion now ?

kinggeorge · Answer

When asking for the inverse of a statement, the question is asking for a specific wording. While it may be true that two different answers have the same meaning, they are worded differently, and so you are looking for 

"If the alternate exterior angles are not congruent, then the lines are not parallel."

since it has the wording you want.

jhonyy9 · Answer

thank you 
so than you wann saying that from these two answers just one ,just second can being accepted correct,right ?

kinggeorge · Answer

Only one of the answers is correct. "Logically equivalent" does not mean "Is the same as."

jhonyy9 · Answer

1. Statement: If p, then q
2. Inverse: If ~p, then ~q
3. Converse: If q, then p
4. Contrapositive: If ~q, then ~p

1 and 4 are equivalent statements; 2 and 4 are equivalent statements.

jhonyy9 · Answer

these answers i have got on my question

jhonyy9 · Answer

LiveforMusic 

how do you think it now ? is it understandably for you ?