Question
Download Solution PDFLet A = {1, 3, 5}, B = {4, 5} and C = {4, 5, 6}. Find A × (B ∪ C).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Union of sets: Let A and B be two sets.
The union of A and B is the set of all those elements which belong to either A or B or both A and B.
The union of A and B is denoted by A ∪ B.
i.e A ∪ B = {x : x ∈ A or x ∈ B}
The Venn diagram for the union of any two sets is 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, 5} and C = {4, 5, 6}
B U C = {4, 5, 6}
A × (B U C) = {1, 3, 5} × {4, 5, 6}
⇒ {(1, 4) (1, 5) (1, 6) (3, 4) (3, 5) (3, 6) (5, 4) (5, 5) (5, 6)}
Last updated on May 31, 2025
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