Another Deductive Reasoning Q: M works late, B makes lunch

[LisaPersad]

Choose the statement below that is not logically equivalent to "If Mary works late, then Bill will prepare lunch."

a. If Bill does not prepare lunch, then Mary did not work late.

b. If Bill prepares lunch, then Mary works late.

My answer:

p and not q therefore, Mary works late and Bill did not prepare lunch.

The question asked, which is not logical.... I think choice A because it is not q and not p.

Is this correct?

 

[Deleted member 4993]

Choose the statement below that is not logically equivalent to "If Mary works late, then Bill will prepare lunch."

a. If Bill does not prepare lunch, then Mary did not work late.

b. If Bill prepares lunch, then Mary works late.

My answer:

p and not q therefore, Mary works late and Bill did not prepare lunch.

The question asked, which is not logical.... I think choice A because it is not q and not p.

Is this correct?

Statement 'a' is contra-positive of the original statement.

 

[soroban]

Hello, LisaPersad!

Choose the statement below that is not logically equivalent to:
. . "If Mary works late, then Bill will prepare lunch."

(a) If Bill does not prepare lunch, then Mary did not work late.

(b) If Bill prepares lunch, then Mary works late.

\(\displaystyle \text{We have: }\;\text{If }\underbrace{\text{Mary works late}}_p\text{, then }\underbrace{\text{Bill prepares lunch.}}_q\)


\(\displaystyle \text{Statement (a) is: }\;\text{If }\underbrace{\text{Bill does not prepare lunch,}}_{\sim q} \underbrace{\text{ then }}_{\to}\underbrace{\text{Mary did not work late.}}_{\sim p}\)

. . This is the contrapositive which is logically equivalent.



\(\displaystyle \text{Statement (b) is: }\;\text{If } \underbrace{\text{Bill prepares lunch,}}_q \underbrace{\text{ then }}_{\to}\underbrace{\text{Mary works late.}}_p\)

. . This is the converse, which is not logically equivalent.



The answer is: statement (b).