Question:

If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:
(i) A = {a, b, c}
(ii) B = {d, e, f, g}
(iii) C = {a, c, e, g}
(iv) D = {f, g, h, a}

Updated On: Aug 6, 2024
Hide Solution
collegedunia
Verified By Collegedunia

Solution and Explanation

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

(ii) B = {d, e, f, g}
∴ B' = {a, b , c , h}

(iii) C = {a, c, e, g}
∴ C' = {b, d, f, h}

(iv) D = {f, g, h, a}
∴ D' = {b, c,d,e}

Was this answer helpful?
2
0

Top Questions on Complement of a Set

View All

Questions Asked in CBSE Class XI exam

View More Questions

Concepts Used:

Complement of a Set

The complement of a set is described as A’ = {x: x ∈ U and x ∉ A}

where,

A’ stands for the complement.

Complement of Sets Properties:

1. Complement Laws: The union of a set A and its complement A’ allows the universal set U of which, A and A’ are a subset.

A ∪ A’ = U

Also, the intersection of a set A and its complement A’ cause the empty set ∅.

A ∩ A’ = ∅

For Example: If U = {11, 12 , 13 , 14 , 15 } and A = {11 , 12 , 13 } then A’ = {14 , 15}. From this it can be seen that

A ∪ A’ = U = { 11 , 12 , 13 , 14 , 15}

Also, A ∩ A’ = ∅

2. Law of Double Complementation: According to the law, if we take the complement of the complemented set A’ then, we get the set A itself.

(A’)’ = A

In the previous example we can see that, if U = {11 , 12 , 13 , 14 , 15} and A = {11 , 12, 13} then A’ ={14 , 15}. Now if we consider the complement of set ‘A’ we get,

(A’)’ = {11 , 12 , 13} = A

This gives back the set A itself.

3. Law of empty set and universal set: According to this law the complement of the universal set gives us the empty set and vice-versa i.e.,

∅’ = U And U’ = ∅

This law is accessible.