If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is a universal set and A = {1, 3, 5, 7, 9} then find the cardinality 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 A^c such that A’ = {x: x ∉ A} = U – A, where U is the universal set

CALCULATION:

Given: U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is a universal set and A = {1, 3, 5, 7, 9}

Here, we have to find A'

As we know that, A’ = {x: x ∉ A} = U – A, where U is the universal set

⇒ A' = U - A = {2, 4, 6, 8, 10}

As we know that, if set A has m elements in it then the cardinality of set A is given by n(A) = m

⇒ n(A') = 5

Hence, correct option is 2.