Question

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A and B have 3 elements in common then find the number of common elements in AXB and BXA?
O 12
06​

Answer 1

Given:

A and B have 3 elements in common

To Find:

Number of common elements in AXB and BXA

Solution:

Let A = {a,b,c,d,e} and B = {1,2,3,4}

So,

A×B = { (a,1), (a,2), (a,3), (a,4), (b,1), (b,2), (b,3), (b,4), (c,1), (c,2), (c,3), (c,4), (d,1),(d,2), (d,3), (d,4), (e,1), (e,2), (e,3), (e,4) }

∴n(A×B) = n(A)n(B) = 20

We know that

(A×B)∩(B×A) = (A∩B)×(B∩A)

Common elements of A and B = 3

∴n(A∩B)=3

So,

n[(A∩B)×(B∩A)] = n(A∩B)n(B∩A) = 3×3 = 9 elements

∴n[(A∩B)×(B∩A)]=9 elements

Hence, AxB and BxA have 9 elements in common.