## Related questions with answers

Let U={1, 2, 3, 4, 5, 6, 7, 8}, A={2, 4, 6}, B={1, 2, 5, 8}, and C={1, 3, 7}. Find each of the following.

$\left( A ^ { \prime } \cap B \right) ^ { \prime }$

Solutions

VerifiedGiven that $U = \{1, 2, 3, 4, 5, 6, 7, 8\},$ $A = \{2, 4, 6\}$ and $B = \{1, 2, 5, 8\}.$

Now $A'$ is the set which contains all the elements of $U$ that does not belong to $A.$ We see that $1, 3, 5, 7$ and $8$ are the only elements of $U$ that does not belong to $A.$ Thus $A' = \{1, 3, 5, 7, 8\}.$

Now $A' \cap B$ is the set that contains all the elements that belong to $A'$ and $B$ both. Now we see that $1, 5$ and $8$ are the elements which belongs to both $A'$ and $B$. Therefore $A' \cap B = \{1, 5, 8\}$

Now $(A' \cap B)'$ is the set which contains all the elements of $U$ that does not belong to $A' \cap B.$ We see that $2, 3, 4, 6$ and $7$ are the only elements of $U$ that does not belong to $A' \cap B.$ Thus $(A' \cap B)' = \{2, 3, 4, 6, 7\}.$

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