Daily Drills 3 - Section 3 - Question 4

Supply the missing premise that makes the conclusion follow logically:P: X–some–YP: ?C: Z–some–Y

chayse September 23, 2019

True

Why can't the first answer be true?

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Skylar September 28, 2019

@chayse Happy to help. Let's take a look.

P: X-some-Y
Y-some-X
P: ?
C: Z-some-Y
Y-some-Z

Since both are some statements with Y, we know that we need to connect X and Z. We would do this as X ->Z. This is because we know we need an S->N statement to make a valid deduction (except in the case of two most statements with their left side in common), and we know that the arrow must point away from the quantifier/the S condition must be shared. This is why answer choice (A) is incorrect.

However, X -> Z is not an answer choice, so we must find its contrapositive (which has the same meaning). To do this, we reverse and negate to get: not Z -> not X. This is answer choice (C).

Does this make sense? Please let me know if you have any other questions!

sarahmadelinesantos November 8, 2019

This is helpful, thank you!