Question

Refer to the following conditional statement:
If a and b are odd integers, then a – b is an even integer.
Identify the hypothesis.

A. a – b is not an even integer
B. a and b are not odd integers
C. a and b are odd integers
D. a – b is an even integer

Answer 1

I think its C

Answer 2

@whpalmer4

Answer 3

Yes that is correct

Answer 4

Ok, thanks

Answer 5

Refer to the following conditional statement:

If a and b are odd integers, then a • b is an odd integer. Which is the inverse of the statement?

A. a • b is an odd integer
B. If a • b is an odd integer, then a and b are odd integers.
C. If a and b are not odd integers, then a • b is not an odd integer.
D. a and b are odd integers

I think it's C.

Answer 6

@BlackLabel

Answer 7

Yup that is correct

Answer 8

If p then q
Inverse: If ~p then ~q

Answer 9

Oh, then B? O.O

Answer 10

Wait, thats not right

Answer 11

Ya, its C

Answer 12

Right?

Answer 13

Yup

Answer 14

You got it right I was just giving you the definition of an inverse statement

Answer 15

Ok, thanks!
Can you help with a few more?

Answer 16

Ya np. Just working at the same time so it may take a lil longer to respond

Answer 17

Ok, thanks!

Refer to the following conditional statement:
If a and b are odd integers, then a • b is an odd integer.

Which is the contrapositive of the statement?

A. If a • b is not an odd integer, then a and b are not odd integers.
B. If a • b is an odd integer, then a and b are odd integers.
C. a • b is an odd integer
D. a and b are odd integers

Answer 18

I would say B

Answer 19

Oh wait.. actually, A

Answer 20

Yup it is A

Answer 21

Sorry! XP

Answer 22

What kind of reasoning is Kim using?

Kim notices that 24 = 6 + 18, 63 = 9 + 54, 39 = 12 + 27, and 72 = 9 + 63, so she thinks it is likely that she can write every number divisible by 3 as the sum of two numbers divisible by 3.

A. deductive
B. inductive
C. hypothesis
D.conclusion

Answer 23

B?

Answer 24

Yup I guess we can say inductive

Answer 25

That is the most apropo even though we usually can not induce like that when proving

Answer 26

Ok, thanks!

What kind of reasoning is used here?

If a = b and c = d, then a • c = b • d.

A. hypothesis
B. conclusion
C. deductive
D. inductive

I think this is C

Answer 27

@BlackLabel

Answer 28

I think so too since this is more general

Answer 29

Yup, thanks! How about this one?

Which is a counterexample that disproves the following statement?
For all integers x, 1/x \[\le\] x

A. x = 5
B. x = 100
C. x = 2
D. x = 0.5

Answer 30

Oh, my bad, the:
\[\le\]
Should be after 1/x and before x, like this: 1/x <_ x

Answer 31

I'm not sure about this question.. can you explain?

Answer 32

Maybe D..?

Answer 33

Ok basically the statement is saying that for any integers x then \( \frac{1}{x}\) will always be smaller than or equal to x
Now we need to find an example where this is not the case
BUt the statement is true for 100 since 1/100<100
and 1/5<5
and 2< 1/2
Now the issue with .5 is that .5 is not an integer.
.5 is a fraction and the question specifically states that x must be ab integer

Answer 34

1/.5=2
so .5<1/.5
But .5 is not an integer
So D would be my preferred option eventhough its not really true

Answer 35

Ah, I see! Then D it is?

Answer 36

It really isnt D but just go for it anyways

Answer 37

Btw, did you realize that the question says:

Which is a counterexample that DISPROVES the following statement?

Answer 38

Do, if you say it isn't D, then for this question, it IS D?

Answer 39

Yaaaa I got that
None of them disprove the statement
In order to disprove the statement The hypothesis must be true which is that x must be an integer. Since x is not an integer then x can not qualify to disprove the statement

Answer 40

I mean So*

Answer 41

Then its still D?

Answer 42

Lets go for D. They may have worded the question in correctly and meant to say ration number instead of integer

Answer 43

rational number*

Answer 44

Alright then! Thanks


What is the reason for Statement 2?

A. addition property of equality
B. property of opposites
C. identity property of addition
D. associative property of addition

Answer 45

Is it B?

Answer 46

addition property of opposites

The property that states the sum of a number and its opposite is always zero.

Answer 47

Yup that is what I was thinking

Answer 48

Only one that makes most sense

Answer 49

Ok, thanks :) This one:

Write the contrapositive of the conditional statement and then determine if the conditional statement and the contrapositive are true or false.

If 6x ≠ 24, then x ≠ 4.

A. If 6x = 24, then x = 4. The conditional statement and the contrapositive are both true. B. If x = 4, then 6x = 24. The conditional statement and the contrapositive are both true. C. If x = 4, then 6x = 24. The conditional statement is false, and the contrapositive is true. D. If x ≠ 4, then 6x ≠ 24. The conditional statement and the contrapositive are both false.

Answer 50

Oh, sorry, its all mixed up O.O

A. If 6x = 24, then x = 4. The conditional statement and the contrapositive are both true.

B. If x = 4, then 6x = 24. The conditional statement and the contrapositive are both true.

C. If x = 4, then 6x = 24. The conditional statement is false, and the contrapositive is true.

D. If x ≠ 4, then 6x ≠ 24. The conditional statement and the contrapositive are both false.

Answer 51

I think B

Answer 52

My bad, I meant A

Answer 53

Im not sure Im flirting btwn A and B
Lemme think abt this

Answer 54

Ok

Answer 55

"A" definitely sounds more correct. So I would go with A but maybe post another question and get someone to take a look at this

Answer 56

Aren't A and B almost the same thing? I mean, all they did was switch these around:

If 6x = 24, then x = 4.

Answer 57

Ok, thanks :) I'll do that!

Answer 58

I would like to disagree the if part is the hypothesis:

"A very closely related logical meaning is that for any statement or claim of the form "if A, then B", A is said to the be hypothesis of the claim. This usage transfers the idea of a "hypothesis" from the argument that establishes A⇒B to the naked assertion that A⇒B. "Assumption" is possible here, but appears to be less common than "hypothesis", especially if the claim is written symbolically rather than a theorem statement in prose."

Answer 59

You're right, that's the formal logic usage, the hypothesis being the antecedent. I withdraw my objection, though I'll continue to think that's a ridiculous hypothesis :-)