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Que: A set is such that if m is in the set, \(m+3\) is also in the set. If ...

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by Max@Math Revolution » Wed Jun 16, 2021 8:04 pm

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B

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D

E

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Que: A set is such that if m is in the set, \(m+3\) is also in the set. If −2 is in the set, which of the following is also in the set?

I. −2
II. 1
III. 4

(A) Only I
(B) Only II
(C) Only I and II
(D) Only II and III
(E) I, II, and III
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Re: Que: A set is such that if m is in the set, \(m+3\) is also in the set. If ...

by Max@Math Revolution » Thu Jun 17, 2021 8:50 pm
Solution: According to the problem: If m is in the set, (m + 3) is also in the set.

However, it does NOT imply that if (m + 3) is in the set, then m must be in the set.

What it does imply is that: If (m + 3) is NOT in the set, m is NOT in the set.

Thus, if we have m = −2 as a member of the set, m + 3 = (-2) + 3 = 1 is also a member of the set. Thus, statement II is correct.

Proceeding in the same way: Since m = 1 is a member of the set, then m + 3 = 1 + 3 = 4 is a member of the set. Thus, statement III is also correct.

Therefore, D is the correct answer.

Answer D
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