Question 452165: Given the following set, select the statement below that is true.
A = {q, r, s, t, u}
p ∈ A
5 ∈ A
r ∉ A
s ∈ A
A Ø
Answer by Leaf W.(135)   (Show Source):
You can put this solution on YOUR website! Given the following set, select the statement below that is true.
A = {q, r, s, t, u}
p ∈ A
5 ∈ A
r ∉ A
s ∈ A
A Ø
∈ means that something is an element or member of a set. For example, if C = {1, 3, 5, 7}, 3 is within set C, so 3 ∈ C
Therefore, see my reasoning for each possible answer.
==> p ∈ A
This is saying that p is part of set A. However, when you look at the elements of A (A = {q, r, s, t, u}, so the elements of a are q, r, s, t, and u), there is no p, so this is FALSE, and the incorrect answer.
==> 5 ∈ A
This is saying that 5 is part of set A. However, as said previously, the only elements of A are q, r, s, t, and u--there is no 5 among these. Therefore, this is FALSE, and the incorrect answer.
==> r ∉ A
This is saying that r is an element of set A. However, when you look at the elements of set A (q, r, s, t, and u), there IS an r, so this is FALSE, and the incorrect answer.
==> s ∈ A
This is saying that s is an element of set A. When you look at the elements of set A (q, r, s, t, and u), s IS included, so this is TRUE, and the correct answer.
==> A Ø
This is saying that there are no elements in set A. However, it says before that that A encompasses q, r, s, t, and u, so it must have elements--they are stated right there! Therefore, this is FALSE, and the incorrect answer.
***Therefore, the correct answer is that s ∈ A
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