Logic Games Random Mix - - Question 15

If history is not offered by the summer program, then which one of the following is another course that CANNOT be off...

MelodyWilson March 17, 2021

Why not E?

I understand how A could be the correct answer, but why couldn’t zoology also be an answer? Is it because of the contrapositive of the last rule that states that either H or Z could not be present without G? Please advise.

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Victoria April 14, 2021

Hi @MelodyWilson,

Happy to help!

Rule 4 tells us that if G is offered, then both H and Z are also offered.

G --> H and Z
Not H OR Not Z --> Not G

The contrapositive does not tell us that either H or Z could not be present without G. Rather, it tells us that, if H or Z is not present, then G cannot be present.

The question stem tells us that H is not offered by the summer program. Therefore, G cannot be offered by the summer program.

L cannot be offered because, if L is offered, then G is also offered. We already know from our deduction above that G cannot be offered by the summer program.

It is fine if Z is offered because there are no conditions precluding it.

We know that Not H OR Not Z --> Not G. We already know that H cannot be offered. Therefore, it does not matter whether Z is offered or not, we know that the summer program cannot offer G.

We learn from Rule 3 that if S is offered, then P is also offered, but Z is not.

S --> P AND Not Z
Not P OR Z --> Not S

Neither of these tell us that Z cannot be offered. Therefore, Z could be offered by the summer program.

Hope this helps! Please let us know if you have any further questions.