Question

Write the following from the given Venn diagram: i) A ∩ B ii) A’ iii) B’ iv) A’ ∩ B’​

Answer 1

Given : Venn diagram

To find : (1) A ∩ B , (2) A' , (3) B' , (4) A' ∩ B'

Solution :

(1)

A ∩ B is the set of all x such that x ∈ A as well as x ∈ B. This property is called intersection of two sets.

So the required set,

A ∩ B = { 1, 3, 7}

(2)

A' is the set of all x such that x belongs to Universal set but doesn't belongs to set A. It is called compliment of a set.

So the required set,

A' = { 4, 6, 10, 13 } ________(1)

(3)

B' is the set of all those elements which belongs to universal set but doesn't belongs to set B.

So, the required set,

B' = { 2, 5, 9, 8 } __________(2)

(4)

Now, A' ∩ B' is the intersection of A' and B' i.e. set of all those elements which belongs to set A' as well as B'.

Required set is intersection of equation (1) and (2),

A' ∩ B' = { }

There is no common element between set A' and B' so the intersection of both the sets is {} empty or phi set.