Sets Test

Result

Sets Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

If A and B are two sets, then A ∩ ( A ∪ B )′ is equal to

A
A

B
B

C
∅

D
none of these

Solution

A ∩ ( A ∪ B )′ = ϕ

since ( A ∪ B )′ Set represent the element which are not belongs to it,so there is no common element with the set A.So the answer is null set
Question 2
1 / -0

If A is any set , then

A
A ∪ A′ = ϕ

B
A ∩ A′ = A

C
A ∩ A′ = U

D
A ∪ A′ = U

Solution

A ∪ A′ = { x ∈ U: x ∈ A } ∪ { x ∈ U: x ∉ A } = U
Question 3
1 / -0

If A and B be any two sets , then ( A ∪ B )′ is equal to

A
A′ ∪ B′

B
A ∩ B

C
A ∪ B

D
A′ ∩ B′

Solution

x ∈ ( A ∪ B )′

⇒x ∉ ( A ∪ B )

⇒x ∉ A or x ∉ B

⇒ x ∈ A′ and x ∈ B′

⇒x ∈ A′ ∩ B′

⇒( A ∪ B )′ ⊆ A′ ∩ B′

Similarly we can show ( A′ ∩ B ′) ⊆ ( A ∪ B )′

so ( A ∪ B )′ = ( A′ ∩ B′ )
Question 4
1 / -0

Let A = { 1,2,3,4} , B = { 2,3,4,5,6 } , then ( A ∩ B ) is equal to :

A
{ 1,2,3 }

B
{ 1 }

C
{ 2,3,4 }

D
{ 5,6 }

Solution

Here A = { 1,2,3,4} and B = {2,3,4,5,6}

A ∩ B = {1,2,3,4} ∩ {2,3,4,5,6}

={2,3,4}