Question

I am not certain of this answer
17.
@jim_thompson5910

Answer 1

17 is a very fun logic question!

Answer 2

hint for #17: one of those statements has a contrapositive that is very useful

Answer 3

If it's not q, then it's not p.
Now it only says it was Friday, it does not state that he met with his friends :/
@jim_thompson5910

Answer 4

so, it's friday

Answer 5

walk through what it means

Answer 6

personally, i disagree with the answers, but i know which they want

Answer 7

How do I know if he ordered pizza when I don't know if he met his friends ? :/

Answer 8

so, what is the first thing you know for certain?

Answer 9

It's Friday.

Answer 10

100% true

Answer 11

ok now, the first statement tells us that for every single friday, he plays soccer

Answer 12

what does it mean if he plays soccer?

Answer 13

-If he meets his friends, he orders pizza.

Answer 14

What is the contrapositive of each statement given?

Answer 15

If Luan doesn't play soccer, then it's not Friday.
IF Luan does not order pizza, then Luan did not meet with his friends.
If he does not play soccer, then he did not meet with his friends.

Therefore, Luan will order pizza?

Answer 16

"If he does not play soccer, then he did not meet with his friends." is not the correct contrapositive

Answer 17

It sounds like a converse, but the "it's" and "then it's" format doesn't make sense :/

Answer 18

the original third statement is

"if he does not meet with friends, then he does not play soccer"

Answer 19

flip the two, then negate each piece

so change "he does not play soccer" to "he does play soccer" (notice how I changed the negative to positive)

and same for the other piece

Answer 20

If he does play soccer, he does meet with his friends.

Answer 21

good

Answer 22

so because we know the contrapositive is equivalent to the original, we know that

"if he does not meet with friends, then he does not play soccer"

and

"If he does play soccer, he does meet with his friends."

are equivalent statements

Answer 23

Now let's set up this notation

P: it is friday
Q: he plays soccer
R: he meets his friends
S: he orders pizza

Answer 24

Using that shorthand notation, we can write the first statement as

"If P, then Q"

Answer 25

and using the same notation, we can write the contrapositive of the third statement as

"If Q, then R"

Answer 26

how can you combine "If P, then Q" & "If Q, then R"

Answer 27

If it is friday, then he plays soccer.
If he plays soccer, then he meets his friends .

Answer 28

how can you combine those statements into one statement (of the form "If this, then that")?

Answer 29

If it is friday, then he plays soccer and then meets his friends .
OR If it is friday, then he plays soccer and meets his friends .

Answer 30

Ok let's say we know 100% that it is friday

Answer 31

since that is the case, then we know he plays soccer

and if he plays soccer, then he meets with his friends

Answer 32

so you can see this chain reaction forming: if A, then B, which leads to C

or...we can shorten things and say "if we start with A, then we lead ultimately to C"

Answer 33

which means that if it's friday, then he meets with his friends

Answer 34

^that's called the transitive property :)

Answer 35

Option B is eliminated :)

Answer 36

so if we know it's friday, that leads to us knowing he'll meet with friends

what can you do with this info to get to the next step?

Answer 37

I still believe it's C. Luan will order pizza..

Answer 38

correct

Answer 39

I said that before though.... :/

Answer 40

before you put D as your answer for 17

Answer 41

and in the contrapositive explaining part I put "Luan will order pizza?"
I think the question mark was the bad part- haha..

Answer 42

oh nvm, I see what you mean above

I was referring to an earlier post

Answer 43

yeah I see it now

Answer 44

It's okay- thank you sooo much for explaining :)

Answer 45

!!**

Answer 46

you're welcome