Question

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 1

@whpalmer4

Answer 2

@BlackLabel check this one for me?

The stem-and-leaf plot shows the number of e-mails a business woman received each day during her vacation. Which conjecture is supported by the data?

A. She received 300 emails on one day.
B. She never received fewer than 10 e-mails in one day.
C. On no days did she receive 15 emails.
D. She never received more than 20 e-mails in one day.

Answer 3

I think C

Answer 4

Yup its C

Answer 5

Thanks :) Now if only someone can help with the first question O.O

Answer 6

@BlackLabel can you tag someone that's online and you know is good at this stuff?

Answer 7

@SithsAndGiggles Are you familiar with logic?

Answer 8

It's B.

Answer 9

@SithsAndGiggles The first question, NOT stem and leaf plot :)

Answer 10

Really, why?

Answer 11

Given a conditional statement \(A\Rightarrow B\), its contrapositive is \(\neg B\Rightarrow\neg A\), where \(\neg A\) is the negation of \(A\).

As for why both are true. consider the statement itself. If \(x=4\), then \(6x=24\) must be true. If \(6x\not=24\), then \(x\) can't be 4, otherwise you have equality.

Answer 12

The "if... then" part of A is not the contrapositive of the given statement.

Answer 13

ahhhh you wrote your question differently here -.-

Answer 14

So @BlackLabel you think its B now?

Answer 15

It is def B

Answer 16

Alright, thank you @BlackLabel and @SithsAndGiggles