If U={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}, X={4,8,12,13,14,15} and Y={2,3,4,5,13}, then (X ∩ Y)’ is:a.{4, 13}b.{1,2,3,5,6,7,8,9,10,11,12,14,15}c.{1,2,3,5,6,7,9,10,11}d.{2,3,4,5,13,14,15}
Question
If U={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}, X={4,8,12,13,14,15} and Y={2,3,4,5,13}, then (X ∩ Y)’ is:a.{4, 13}b.{1,2,3,5,6,7,8,9,10,11,12,14,15}c.{1,2,3,5,6,7,9,10,11}d.{2,3,4,5,13,14,15}
Solution
First, let's find the intersection of sets X and Y, denoted as X ∩ Y. The intersection of two sets is the set of elements that are common to both sets.
So, X ∩ Y = {4, 13}
Next, we need to find the complement of this set (X ∩ Y)', which is the set of all elements in the universal set U that are not in (X ∩ Y).
So, (X ∩ Y)' = U - (X ∩ Y) = {1,2,3,5,6,7,8,9,10,11,12,14,15}
Therefore, the answer is b.{1,2,3,5,6,7,8,9,10,11,12,14,15}.
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