Question

Algebra help? :)
Which is the converse of the conditional statement and is true or false?

If a number is a prime number, then it is divisible by 1 and itself.

A.
If a number is not divisible by 1 and itself, then it is a prime number. The converse is false.

B.
If a number is not divisible by 1 and itself, then it is not a prime number. The converse is true.

C.
If a number is not a prime number, then it is not divisible by 1 and itself. The converse is false.

D.
If a number is divisible by 1 and itself, then it is a prime number. The converse is false.

Answer 1

B is good

Answer 2

suely B looks good...

Answer 3

can you help with 4 more?

Answer 4

f corse..

Answer 5

Converse of "If A then B" is "If B then A".

So, it's not B. Let A = "number is prime", so what is B?

Answer 6

I don't think it is B. The converse of B is "If it is not a prime number, the number is not divisible by 1 and the number itself." I don't think the converse of B makes sense.

Answer 7

I just noticed by choice of names for the two claims, A and B, conflicts with the names for the multi-choice answers.

Answer 8

Ooops. So, rephrase: converse of "If P then Q" is "If Q then P". Let Q = "is prime", then P = ?

Answer 9

is also prime?

Answer 10

Let Q = "is prime", then P = "is divisible by 1". Thus, the converse is "If divisible by 1 then is prime". It's just flipping the implication.

Answer 11

oh duh

Answer 12

Notice that the converse of "Is prime -> divisible by 1" is not true, i.e., it's not necessarily the case that something that is divisible by 1 is prime. But, that's alright. The converse is simply not true, while the original implication is.

Answer 13

so D is out?

Answer 14

Well, the answer is D. The converse of "is prime -> divisible by 1" is "is divisible by 1 -> is prime", which is not true. So, D.

Answer 15

oh I thought it was not true.... XD makes way more sense! XD 4 more?

Answer 16

I'll help if I can.

Answer 17

Thanks :)

Answer 18

Welcome.

Answer 19

Which conditional statement has a converse that is true?

A.
If I am reading, then I am sitting.

B.
If I am eating, then I am hungry.

C.
If I am driving, then I am moving.

D.
If I am wet, then I am swimming.

Answer 20

B or D (i think)

Answer 21

So, first, take the converse of each one. Implication A says, "If reading, then sitting." Converse is "If sitting, then reading." Clearly, just because one is sitting, that does not mean he or she is sitting. So, A is out.

Answer 22

B says, "If eating, then hungry", so converse(B) says "If hungry, then eating." Is this true?

Answer 23

Yes

Answer 24

You can't be hungry and not eating? Usually, the reason why you are hungry in the first place is because you have not been eating -- there must be some point in which you are both hungry and not eating, right? :)

Answer 25

Let's look at C and D. "If I am driving, I am moving" -> converse "If I am moving, I am driving." Is this converse true?

Answer 26

true... and I wanna guess D is out due to the fact that you font have to swim to get wet?

Answer 27

yes thats true

Answer 28

Well,let's consider D. Implication: If I am wet, then I am swimming. Converse: If I am swimming, then I am wet. There are cases in which you can imagine not being wet while swimming, but in general this seems really plausible. It seems to be the best one.

Answer 29

If I am moving, then I am driving? I can walk, and thus be moving and not driving. So, C is out.

Answer 30

I did not think of that thanks so ima go with C C:

Answer 31

I mean D
I dont know why I said C

Answer 32

Yes, correct.

Answer 33

Which is the inverse of the conditional statement?

If a number is divisible by 2, then it is a composite number


A.
If a number is a composite number, then it is divisible by 2.

B.
If a number is a composite number, then it is not divisible by 2.

C.
If a number is not divisible by 2, then it is not a composite number.

D.
If a number is not a composite number, then it is not divisible by 2.

Answer 34

Let me look up inverse. Brb.

Answer 35

ok

Answer 36

A = P->Q. Inverse of A is not(P) -> not(Q)

Answer 37

So, let P = "number divisible by 2", and Q = "composite number".

So, inverse. not(P) = "number not divisible by 2", and not(Q) = "not a prime number". What do you think the answer is?

Answer 38

A?

Answer 39

That is the converse. Remember, inverse of P->Q is not(P)->not(Q).

Answer 40

While converse of P->Q is Q->P.

Answer 41

Note that P->Q just means "If P then Q" where P and Q are just statements that can be true or false.

Answer 42

C?

Answer 43

Yup! Good job.

Answer 44

XD Yay! :) 3 more? :D

Answer 45

Sure, but I would like for you to try to answer it yourself -- show me your work, as it were -- and I will step to guide you and give you hints if needed.

Answer 46

ok :) good deal :D

Answer 47

Write the contrapositive of the conditional statement.

If an animal is a fish, then it lives in water.

A.
If an animal is not a fish, then it does not live in water.

B.
If an animal does not live in water, then it is not a fish.

C.
If an animal lives in water, then it is a fish.

D.
If an animal does not live in water, then it lives in water.

Answer 48

Ok, first, let's define contrapositive. Can you define it in terms of P and Q?

Answer 49

ugh.... If an animal does not live in water, then it is not a fish. (the contrapositive of (if p then q) is (if not q then not p))? I think...

Answer 50

Good, nice work! You got it.

Answer 51

I know D doesn't make any sense what's so ever and oh... AWESOME! XD

Answer 52

Note that the contrapositive of a true statement is also a true statement.

Answer 53

I'll keep that in mind ;)

Answer 54

LOL

Answer 55

I think it's one of Sherlock's trump cards.

Answer 56

Im really gonna your help on this one >.<

Which shows the contrapositive of the conditional statement, and if the conditional statement and the contrapositive are true or false?

If x – 7 ≠ 10, then x ≠ 17.


A.
If x – 7 = 10, then x = 17. The conditional statement and the contrapositive are both true.

B.
If x ≠ 17, then x – 7 ≠ 10. The conditional statement and the contrapositive are both false.

C.
If x = 17, then x – 7 = 10. The conditional statement is false and the contrapositive is true.

D.
If x = 17, then x – 7 = 10. The conditional statement and the contrapositive are both true.

Answer 57

I think I can do this :) ... maybe

Answer 58

Ok, so first, let's identify P and Q in the implication "If P then Q".

Answer 59

What do you think P is?

Answer 60

at "x = 17"?

Answer 61

P is "x - 10 != 7". What do you think Q is? Note that I am not yet asking about the contrapositive.

Answer 62

Err, P is "x - 7 != 10"

Answer 63

ugh is it "x = 7"? Like I said... im not good at this but I dont know any other place for it

Answer 64

No problem. Ok, looks like you may be a little confused about what I'm asking for. I was just trying to get us to recognize what the P and Q should be in the statement "If x - 7 != 10 then x != 17". That is, I wanted to fit it to the pattern "If P then Q".

P, then, is "x - 7 != 10" and Q is "x != 17".

Now, we know that contrapositive is "not P then not Q". It is not a simple matter of "taking the opposite" of the P and Q we have identified previously.

Answer 65

Err, "it is not a simple matter of..." should say "it is NOW a simple matter of"... Sorry about that.

Answer 66

ok I think im getting back on track

Answer 67

Also, contrapositive would be "not Q then not P". Boy! I'm full of mistakes. Sorry if I've confused you. Hard to keep the P's and Q's straight!

Answer 68

nah its good, Im always confused XD see were good :) It will hit me eventually ;)

Answer 69

Ok, so P is "x - 7 != 10" and Q is "x != 17". So, not(Q) is "x = 17", and not(P) is "x - 7 = 10".

Answer 70

One final step, right? First, "if x = 17, then x - 7 = 10". Is that true?

Answer 71

yes! I hope XD

Answer 72

Yup, it's true. Also, is the original statement true?

Answer 73

no

Answer 74

right?

Answer 75

The only way x - 7 can equal 10 is if x = 17. However, we are given that x - 7 does not equal 10... so?

Answer 76

Oh, you answered already. Yup.

Answer 77

You are correct.

Answer 78

Oh, wait.

Answer 79

You're not right. :p The statement "If x - 7 != 10 then x != 17" is true.

Answer 80

XD Yay so it's C

Answer 81

Nope, they're both true. :p

Answer 82

Logic can be confusing. If x - 7 != 10, then x CANNOT be 17 right?

Answer 83

If it were to = 10 then yes?

Answer 84

If x - 7 = 10, then x = 17 would be true.

Answer 85

"If x - 7 = 10, then x != 17" is false though.

Answer 86

so It can

Answer 87

and the answer is A?

Answer 88

You're really close! Remember, the contrapositive also flips the P and Q, i.e., if P -> Q becomes "if not Q then not P"

Answer 89

You're almost done. I promise. :)

Answer 90

ITS D!

Answer 91

Yup!

Answer 92

I think after that one we need a quick tea break. :) BRB, gonna get something to drink.

Answer 93

But post your next problem and give me your thoughts on it (assuming either of us still have any brain power left).

Answer 94

YES! I feel great! XD got the hang of it.... sortof XD
and I GOT 100% XD Thank you soo much for taking your time to explain all that to me :)

Answer 95

xD that comment doe I dont have anymore unless I start another lesson.. want me to?

Answer 96

Ok, good job!

Answer 97

I think it's started to click for you. It just takes some getting use to.

Answer 98

Once you can rephrase these kind of logic questions in terms of variables like P and Q, logic becomes just another sort of math and they can be extreme complex but it's not problem.