Question

Which of the following is the contrapositive of the statement "If it is raining, then I will take my umbrella"?

Answer 1

do you know the converse of the statement?

Answer 2

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.

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

is it negative or positive?

Answer 7

is what negative or positive?

Answer 8

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

Answer 9

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

Answer 10

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?

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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.

Answer 17

the books has it at negation .

Answer 18

at least the ones I read

Answer 19

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

Answer 20

what book do you use?

Answer 21

umm... let me look it up

Answer 22

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

Answer 23

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