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.

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.

AB = {1,2,3,4}
{3,4,5,6,7}

AB =
{1,2}

BC = {3,4,5,6,7}
{6,7,8,9}

BC =
{3,4,5}

BA = {3,4,5,6,7}
{1,2,3,4}

BA =
{5,6,7}