Edunes Online Education
Class 11 | CBSE | MATHEMATICS
SETS | COMPLEMENT OF SETS
1.10 Complement of a Set
Let U be the universal set consisting of
all prime numbers.
Let A be a subset of U which consists of all those prime
numbers that are not divisors of 42.
Mathematical description:
A = { x : x ∈ U and x is not a divisor of 42 }
We observe that:
- 2 ∈ U but 2 ∉ A (because 2 divides 42)
- 3 ∈ U but 3 ∉ A (because 3 divides 42)
- 7 ∈ U but 7 ∉ A (because 7 divides 42)
These are the only prime divisors of 42.
Hence, the set of prime numbers that belong to U but
do not belong to A is:
{ 2, 3, 7 }
This set is called the Complement of A with respect to U and is denoted by A′.Complement of A
Definition:
Let U be the universal set and A be a subset of U.
Then the complement of A is the set of all elements of
U which are not elements of A.
A′ = { x : x ∈ U and x ∉ A }
A′ = { x : x ∈ U and x ∉ A }
Clearly, the complement of a set can also be viewed as the
difference between the universal set and the given set.
A′ = U − A
Memory Trigger:
Think of the complement as “everything inside the universe but outside the set”.
Your brain naturally understands this as a visual exclusion.