how do you find the inverse and contrapositive of if you are a quarterback, then you play football

Question

jim_thompson5910 · Answer

Hint:

Original Conditional Statement:  If P, then Q

Inverse: If not P, then not Q

Contrapositive:  If not Q, then not P

jim_thompson5910 · Answer

hopefully that helps

if not, then let me know

anonymous · Answer

i dont really understand how to put it into the sentence but i know what you mean

jim_thompson5910 · Answer

well the original statement "if you are a quarterback, then you play football"

would have

P = you are a quarterback
Q = you play football

anonymous · Answer

would it be if you are not a quarterback then you are not a football player?

jim_thompson5910 · Answer

good that is the inverse

anonymous · Answer

the the contrapositive would be if you are not a football player then you are not a quarterback?

jim_thompson5910 · Answer

perfect

jim_thompson5910 · Answer

silly and subtle difference but "football player" could be replaced with "plays football"

but it's not really that big a deal

anonymous · Answer

okay one more question what would be the counter example?

jim_thompson5910 · Answer

counter example for the original statement? or inverse? contrapositive? 

I'm not sure what exactly they want

anonymous · Answer

it just says if false then write the counter example

jim_thompson5910 · Answer

can I see the full question?

ideally a screenshot works best

anonymous · Answer

Sure one second

jim_thompson5910 · Answer

thanks

anonymous · Answer

attachment

jim_thompson5910 · Answer

"if you are a quarterback, then you play football"

is that statement true or false?

anonymous · Answer

true

jim_thompson5910 · Answer

good, how about the converse

"if you play football, then you are a quarterback"

is that true or false?

anonymous · Answer

False

jim_thompson5910 · Answer

how do you know it's false

anonymous · Answer

Because quarterback isnt the only position?

jim_thompson5910 · Answer

you could say "There are a lot of football positions. For instance, someone at the running back position also plays football. So just because you're a football player, that doesn't automatically make you a quarterback"

that is a counterexample....the existence of something that makes the statement false (ie the example that makes it false)

anonymous · Answer

Thank you so much !

jim_thompson5910 · Answer

you're welcome

you need to do this for the other two as well, but I'm sure you know what to do