Question

Read the statement shown below.

“If Jessica is in Grade 8, then Amy is in Grade 9.”

Which of these is logically equivalent to the above statement?
Answer

If Jessica is not in Grade 8, then Amy is in Grade 9.

If Amy is in Grade 9, then Jessica is not in Grade 8.

If Amy is not in Grade 9, then Jessica is not in Grade 8.

If Jessica is in Grade 8, then Amy cannot be in Grade 9.

Answer 1

The third one is the inverse. Inverse is always logically equivalent. !!

Answer 2

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

Answer 3

If Amy is not in Grade 9, then Jessica is not in Grade 8

Answer 4

what myko said

Answer 5

@myko Yes. @satellite73 Yeah, contrapositive and inverse, but we don't have a contrapositive here.

Answer 6

If amy is not in Grade 9, then jessica is not in grade 8

Answer 7

Oh lol, it is the contrapositive not the inverse.

Answer 8

Statement: If P then Q.

Contrapositive: If not Q then not P.

Inverse: If not P then not Q.

Answer 9

3rd one.

Answer 10

actually we do
statement
if P then Q
converse
if Q then P
inverse
if not P then not Q
contrapositive
if not Q then not P

statement is equivalent to contrapositive
converse is equivalent to inverse

Answer 11

Thank you all!

Answer 12

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