## anonymous one year ago Which of the following is the contrapositive of the statement "If it is raining, then I will take my umbrella"?

1. UsukiDoll

do you know the converse of the statement?

2. UsukiDoll

So, our original statement is if it's raining, then I will take my umbrella IF P THEN Q the negation is if it's not raining, then I will not take my umbrella IF NOT P THEN NOT Q what do we need to do to get the converse of the statement? We need this statement before getting the contrapositive.

3. anonymous

The converse would be if i take my umbrella, then it is raining.

4. UsukiDoll

yes.... now the contrapositive is like the negation...

5. UsukiDoll

the negation is a negative version of the original statement the contrapositive is a ???????????? version of the converse statement

6. UsukiDoll

is it negative or positive?

7. anonymous

is what negative or positive?

8. UsukiDoll

the contrapositive .... I'm asking if it's negative or positive? It can only go one way

9. UsukiDoll

so original statement - positive negation statement - negative converse statement - positive contrapositive statement - ?

10. UsukiDoll

The converse statement is if Q then P If I take my umbrella, then it's raining. that's a positive statement what's the opposite of positive?

11. freckles

oh your negation statement is actually the inverse statement the negation statement of if p then q is p and not q but yeah to find the contrapositive you could find the converse of the inverse that should work

12. UsukiDoll

I thought it goes like this Original Statement If P then Q Negation If NOT P then NOT Q Converse IF Q then P Contrapositive If NOT Q then NOT P

13. freckles

i'm just saying you are given the wrong title for the if not p then not q thing but everything else looks great

14. UsukiDoll

that is in my book. the same book I used for my class

15. UsukiDoll

one of the very few things I understood... x.x ! ! ! !

16. freckles

http://hotmath.com/hotmath_help/topics/converse-inverse-contrapositive.html http://www.regentsprep.org/regents/math/geometry/gp1/negatecompound.htm hmmm... then I guess the titles aren't universal? not sure about that.

17. UsukiDoll

the books has it at negation .

18. UsukiDoll

at least the ones I read

19. freckles

I guess it is up to the OP to get his definition of negation and inverse so we can better help him.

20. freckles

what book do you use?

21. UsukiDoll

umm... let me look it up

22. UsukiDoll

Passage to Abstract Mathematics was the book I used for my course

23. freckles

It seems like your book defines it like all the other text I know look at page 18 example 1.4.5. though I don't see anywhere they mention the inverse statement