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# Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find (B-C)'.

A set is a distinct collection of objects and elements that can be represented in a roaster form or set builder form.

## Answer: If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6} then ( B - C )' = {1, 3, 4, 5, 6, 7, 9}

See detailed solution.

**Explanation:**

Given that universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9},

A = {1, 2, 3, 4},

B = {2, 4, 6, 8} and

C = {3, 4, 5, 6}

As we know that ( B - C ) = B - ( B ∩ C )

B ∩ C means common elements of set B and set C.

B ∩ C = { 2, 4, 6, 8 } ∩ {3, 4, 5, 6}

= { 4, 6 }

B - ( B ∩ C ) means subtracting the elements of set ( B ∩ C ) from set B.

B - ( B ∩ C ) = { 2, 4, 6, 8 } - { 4, 6 }

= { 2, 8 }

We know that ( B - C )' = U - ( B - C )

( B - C )'

= {1, 2, 3, 4, 5, 6, 7, 8, 9} - { 2, 8 }

= {1, 3, 4, 5, 6, 7, 9}

### Thus, If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}, then ( B - C )' = {1, 3, 4, 5, 6, 7, 9}.

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