Question

# If U = $\left\{ 1,2,3,4,5,6,7,8 \right\}$ and A = $\left\{ 2,4,6,8 \right\}$ , find :(a). A’(b). (A’)’

Hint: First we will write the definition of complement of a set and then we will use that to solve the above question and for the part we can use the same method or property.

Universal set: The set containing all objects or elements and of which all other sets are subsets.
Complement of a set: Complement of a set A, denoted by A’, is the set of all elements that belongs to the universal set but does not belong to set A.
When we subtract two sets the common elements of the set which is being subtract is removed and the remaining elements is the final answer.
Now we will solve (a),
Now A’ will be,
U – A = $\left\{ 1,3,5,7 \right\}$
Hence we have found the value of (a).
Now we will solve (b).
Now (A’)’ will be,
U – A’ = $\left\{ 2,4,6,8 \right\}$
Hence, we have also found the value of (b).
Hence we have found the required value.

Note: One should be careful of the fact that when we subtract two sets the common elements of the set which is being subtract is removed and the remaining elements is the final answer, hence this point must be kept in mind to avoid any mistake. We can also solve the part (b) by using the property of complement of set, (A’)’ = A. And from the answer that we have got we can see that this property holds.