Question

Let A = {1,2,3} and B = {2,3,4}. Determine the following:

(a) (A X B) ∩ (B X A)

(b) (A ∩ B) X (B ∩ A)

Answer 1

Answer: A b 2.2]

Explanation:

Answer 2

a)
`(A* B)\cap (B* A)=\{(2,2),(3,3),(2,3),(3,2)\}`

b)
`(A\cap B)* (B\cap A)=\{(2,2),(2,3),(3,2),(3,3)\}`

Explanation:

Given : Let A = {1,2,3} and B = {2,3,4}.

To find : Determine the following

a)
`(A* B)\cap (B* A)`

b)
`(A\cap B)* (B\cap A)`

Solution :

a)
`(A* B)\cap (B* A)`

`A* B=\{a,b\}|a\in A,b\in B`

`A* B=\{(1,2),(1,3),(1,4),(2,2),(2,3),(2,4),(3,2),(3,3),(3,4)\}`

`B* A=\{(2,1),(2,2),(2,3),(3,1),(3,2),(3,3),(4,1),(4,2),(4,3)\}`

`(A* B)\cap (B* A)=\{(2,2),(3,3),(2,3),(3,2)\}`

b)
`(A\cap B)* (B\cap A)`

`A\cap B=\{2,3\}`

`B\cap A=\{2,3\}`

`(A\cap B)* (B\cap A)=\{(2,2),(2,3),(3,2),(3,3)\}`