Question
Download Solution PDFLet A = {1, 3, 5}, B = {4, 6} and C = {5, 6, 7}. Find A × (B ∩ C)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Intersection of sets:
Let A and B be two sets. The intersection of A and B is the set of all those elements which are present in both sets A and B.
The intersection of A and B is denoted by A ∩ B
i.e A ∩ B = {x : x ∈ A and x ∈ B}
The Venn diagram for intersection is as shown below:
Cartesian Product: The Cartesian product of two sets A and B, denoted A × B, is the set of all possible ordered pairs where the elements of A are first and the elements of B are second.
In set-builder notation, A × B = {(a, b) : a ∈ A and b ∈ B}.
Calculation:
Given: A = {1, 3, 5}, B = {4, 6} and C = {5, 6, 7}
B ∩ C = {6}
A × (B ∩ C) = {1, 3, 5} × {6}
⇒ {(1, 6) (3, 6) (5, 6)}
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