# 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.

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### 2 Answers

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,...}**

**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}**

U = N

A = (1,2,3,4).

Complement of A is the set N-A + {5,6,7,8,....}

B= (3,4,5,6,7).

Complement of B is N -B = {1,2} U {8,9,10,11,....}

C = (6,7,8,9).

The complement of C is N-C = { 1,2,3,4,5}U {10,11,,12,...}

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

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

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