Question

Consider A= {1, 2} and B = {2,3} then which of
the following options is correct?
​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Consider Consider A= {1, 2} and B = {2,3} then which of

the following options is correct

a) P(A ∪ B) ≠ P(A) ∪ P(B)

b) P(A ∪ B) = P(A) ∪ P(B)

c) P(A ∪ B) = P(A) ∩ P(B)

d) None of these

EVALUATION

We know that for any set A the set containing all subsets of A is called Power set of A and denoted by P(A)

Here it is given that

A= {1, 2} and B = {2,3}

Thus we get

P(A) = { Φ , { 1 } , { 2 } , { 1 , 2 } }

P(B) = { Φ , { 2 } , { 3 } , { 2 , 3 } }

A ∪ B = { 1 , 2 , 3 }

P(A∪B)

= { Φ , { 1 } , { 2 } , { 3} , { 1 , 2 } , { 2, 3} , { 1 , 3 } , { 1 , 2 , 3 } }

P(A) ∪ P(B)

= { Φ , { 1 } , { 2 } , { 3} , { 1 , 2 } , { 2, 3} }

P(A) ∩ P(B)

= { Φ , { 2 } }

Thus we have P(A ∪ B) ≠ P(A) ∪ P(B)

FINAL ANSWER

Hence the correct option is

a) P(A ∪ B) ≠ P(A) ∪ P(B)

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ If n(A) = 300, n(A∪B) = 500, n(A∩B) = 50 and n(B′) = 350, find n(B) and n(U).

https://brainly.in/question/4193770

2. If A, B and C are any three sets

then prove the following using venn-diagram

A∩(BUC) = (A∩B) U (A∩C)

https://brainly.in/question/23234089