Let A = {1, 2}, B = {2, 3} and C = {1, 2, 3}.(a) Indicate whether each of the following statements is true or false and provide a brief explanation.(i) A ∩ B ∈ C
Question
Let A = {1, 2}, B = {2, 3} and C = {1, 2, 3}.(a) Indicate whether each of the following statements is true or false and provide a brief explanation.(i) A ∩ B ∈ C
Solution
The statement is false.
Here's why:
The intersection of sets A and B (A ∩ B) results in the set {2}.
However, when we say A ∩ B ∈ C, we are stating that the set {2} is an element of set C.
In set theory, there's a difference between an element of a set and a subset of a set. The set {2} is not an element of set C. Set C has three elements: 1, 2, and 3.
But, the set {2} is a subset of set C, because all elements of {2} are in set C.
So, A ∩ B ⊆ C would be a true statement, but A ∩ B ∈ C is false.
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