If A = {1, 4, 7, 9} and U = {1, 4, 5, 6, 7, 8, 9, 10} is a universal set then find the cardinality of the complement set of A ?

Question

Question

Answer 1

CONCEPT:

Complement of a set:

Let A be any set. Then complement of A is denoted by A’ or Ac such that A’ = {x: x ∉ A} = U – A, where U is the universal set

CALCULATION:

Given: A = {1, 4, 7, 9} and U = {1, 4, 5, 6, 7, 8, 9, 10} is a universal set

Here, we have to find the cardinality of the complement set of A

So, first let's find out the complement of the given set A.

As we know that, if is a set then complement of A is given by ’ = {x: x ∉ A} = U – A, where U is the universal set

⇒ A' = {5, 6, 8, 10}

As we can see that, there 4 elements in A'

So, the cardinality of the complement set of A is 4 i.e n(A') = 4

Hence, the correct option is 1.