Question

Which of the following is equivalent to the statement below?

If 3x + 1 = 10, then x ≠ 2.

Answer 1

.A) If x ≠ 2, then 3x + 1 = 10.

.B) If 3x + 1 = 10, then x = 2.

.C) If x = 2, then 3x + 1 = 10.

.D) If x = 2, then 3x + 1 ≠ 10.

Answer 2

Put 2 into your formula, what is the answer?

Answer 3

equivalent statement is the contrapositive

Answer 4

contrapositive of
if P then Q is
if not Q then not P

Answer 5

Or listen to him. :P

Answer 6

If 3x + 1 = 10, then x ≠ 2
P: \(3x+1 = 10\)
Q: \(x \neq 2\)

Answer 7

what?

Answer 8

\(\lnot Q: x=2\)
\(\lnot P: 3x+1\neq 10\)

Answer 9

you have a statement of the form "if P then Q"

Answer 10

If x ≠ 2, then 3x + 1 = 10.?

Answer 11

where P is \( 3x+1=10\) and Q is \(x\neq 2\)

Answer 12

no first you have to negate each of these statements

Answer 13

the negation of \(3x+1=10\) is \(3x+1\neq 10\) and the negation of \(x\neq 2\) is \(x=2\)

Answer 14

If x = 2, then 3x + 1 = 10.?

Answer 15

so to recap slowly
P: \(3x+1=10\)
not P: \(3x+1\neq 10\)
Q: \(x\neq 2\)
not Q: \(x=2\)

Answer 16

huh? im confusseed

Answer 17

you need "if not Q then not P"

Answer 18

and since not Q is \(x=2\) then the contrapostive is
"if \(x=2\) then \(3x+1\neq 10\) which is certainly a true statement

Answer 19

a statement "if P then Q" is equivalent to the contrapositive statement "if not Q then not P"

Answer 20

you following or still a mystery?

Answer 21

mystery

Answer 22

ok we start with the original statement
if \(3x+1=10\) then \(x\neq 2\)

Answer 23

it is of the form
if P then Q

Answer 24

what is P?

Answer 25

3x + 1 = 10

Answer 26

ok good
now what is "not P"

Answer 27

if that is not obvious, let me know and i will tell you

Answer 28

x ≠ 2.

Answer 29

If 3x + 1 = 10, then x = 2.