Question

n(A)=7,n(B)=9,n(A∩B)=4 If,then n[(A×B)∪(B×A)]= ​

Answer 1

Answer:

Given,

• n(A) = 7
• n(B) = 9
• n(A ∩ B)=4

To find : -

n[(A×B)∪(B×A)] = ?

We know that ,

(A×B)∪(B×A)

= (A U B)×(B U A)

= (A U B) × (A U B)

♠ So,

★ n[(A×B)∪(B×A)]

= n [ (A U B) × (A U B) ]

= n(A U B) × n(A U B)

= [ n(A) + n(B) - n(A∩B) ] × [ n(A) + n(B) - n(A∩B) ]

= [ 7 + 9 - 4 ] × [ 7 + 9 - 4 ]

= [ 16 - 4 ] × [ 16 - 4 ]

= 12 × 12

= $\boxed{\bold{144}}$

Answer 2

Answer:

n[(AxB)U(BxA)]=144

Step-by-step explanation:

given

• n(A)=7
• n(B)=9
• n(AΠB)=4

n(A U B) =n(A) + n(B) - n(AΠB)

• n(A U B) =7+9-4
• n(A U B) =12

(A x B) U (B x A) =(A U B) x (B U A)

(A U B)=(B U A)

hence

n[(AxB)U(BxA)] = 12x12

= 144