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Symbols
x or U

 Universal set


A Universal set is a set which contains all the elements of all the sets under consideration. It is largest of all sets under consideration.

Complement of the given set is the set of elements in the universal set, other than the given set.


Example 1:
x = {7,8,9,10,11,12,13,14,15}, A = {8,10,12,14}. Find the complement of set A.

Complement of set A = A' = {7,9,11,13,15}

Example 2:
x = {a,b,c,d,e,f,g,h,i}, A = {a,e,i}, B = {b,c,d,e}. Find the following:-

1)A'
A' = {b,c,d,f,g,h}

2)B'
B' = {a,f,g,h,i}

3)A' B'
A' = {b,c,d,f,g,h}, B' = {a,f,g,h,i}
A' B' = {a,b,c,d,f,g,h,i}

4)A' B'
A' = {b,c,d,f,g,h}, B' = {a,f,g,h,i}
A' B' = {f,g,h}

5)A' B
A' = {b,c,d,f,g,h}, B = {b,c,d,e}
A' B = {b,c,d,e,f,g,h}

6)A B'
A = {a,e,i}, B' = {a,f,g,h,i}
A B' = {a,e,f,g,h,i}

7)A' B
A' = {b,c,d,f,g,h}, B = {b,c,d,e}
A' B = {b,c,d}

8)A B'
A = {a,e,i}, B' = {a,f,g,h,i}
A B' = {a,i}

9)(A B)'
A = {a,e,i}, B = {b,c,d,e}
A B = {a,b,c,d,e,i}
(A B)' = {f,g,h}

10)(A B)'
A = {a,e,i}, B = {b,c,d,e}
A B = {e}
(A B)' = {a,b,c,d,f,g,h,i}

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