Suppose UN is the universal set Let A1234 B34567 C6789 Find

Suppose U=N is the universal set. Let A={1,2,3,4}, B={3,4,5,6,7}, C={6,7,8,9}

Find the complements of A,B,C and A-B, B-C, B-A.

Solution

Let\'s recall the definition of the absolute complement.

The complement of a set is the set of elements that belong to the universal set but do not belong to the set.

According to the rule of complement, the complement of A is the set of elements that belong to U but do not belong to A.

U = N

N = {1,2,3,....,n,....}

A = {1,2,3,4}

complement of A = {5,6,7,8,,...,n,...}

B = {3,4,5,6,7}

complement of B = {1,2,8,9,10,....,n,...}

C = {6,7,8,9}

complement of C = {1,2,3,4,5,10,...,n,...}

The difference between 2 sets is the set of elements that belong to the first set but do not belong to the second set.

A\\B = {1,2,3,4} \\ {3,4,5,6,7}

A\\B = {1,2}

B\\C = {3,4,5,6,7} \\ {6,7,8,9}

B\\C = {3,4,5}

B\\A = {3,4,5,6,7} \\ {1,2,3,4}

B\\A = {5,6,7}