SAT Logic
X is a subset of Y and Y is a subset of Z. Which of the following statements must be true?
(A)
If 1 is in Y, then 1 is in X.
(B)
If 2 is in Z, then 2 is in X.
(C)
If 3 is in Z, then 3 is in Y.
(D)
If 4 is in X, then 4 is in Z.
(E)
None of the above
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1 solution
Correct Answer: D
Solution 1:
Tip: If every element in set A is an element in set B , then A is a subset of B .
Since X is a subset of Y which is a subset of Z, thus X is a subset of Z. Hence, if 4 is in X, then 4 is in Z. Thus D is the correct answer.
Solution 2:
Tip: If every element in set A is an element in set B , then A is a subset of B .
Let X = { 4 } , Y = { 4 , 1 } , Z = { 4 , 3 , 2 , 1 } , where X is a subset of Y and Y is a subset of Z.
(A) is not satisfied since 1 is in Y but not in X.
(B) is not satisfied since 2 is in Z but not in X.
(C) is not satisfied since 3 is in Z but not in Y.
(D) is satisfied since 4 is in X, 4 is in Y, and 4 is in Z.
(E) is wrong because (D) is correct.
Incorrect Choices:
(A) , (B) , (C) , and (E)
Solution 2 shows why these choices are wrong.