Question:
Show that \(A ∩ B = A ∩ C\) need not imply B = C.
Show that \(A ∩ B = A ∩ C\) need not imply B = C.
Updated On: Oct 23, 2023
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Solution and Explanation
Let A = {0, 1}, B = {0, 2, 3}, and C = {0, 4, 5}
Accordingly, \(A ∩ B = \){0} and \(A ∩ C =\) {0}
Here, \(A ∩ B = A ∩ C = \){0}
However, \(B ≠ C [2 ∈ B \) and \(2 ∉ C]\)
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Concepts Used:
Operations on Sets
Some important operations on sets include union, intersection, difference, and the complement of a set, a brief explanation of operations on sets is as follows:
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