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) $(A\times B)\cap (B\times A)=\{(2,2),(3,3),(2,3),(3,2)\}$

b) $(A\cap B)\times (B\cap A)=\{(2,2),(2,3),(3,2),(3,3)\}$

Step-by-step explanation:

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

To find : Determine the following

a) $(A\times B)\cap (B\times A)$

b) $(A\cap B)\times (B\cap A)$

Solution :

a) $(A\times B)\cap (B\times A)$

$A\times B=\{a,b\}|a\in A,b\in B$

$A\times B=\{(1,2),(1,3),(1,4),(2,2),(2,3),(2,4),(3,2),(3,3),(3,4)\}$

$B\times A=\{(2,1),(2,2),(2,3),(3,1),(3,2),(3,3),(4,1),(4,2),(4,3)\}$

$(A\times B)\cap (B\times A)=\{(2,2),(3,3),(2,3),(3,2)\}$

b) $(A\cap B)\times (B\cap A)$

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

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

$(A\cap B)\times (B\cap A)=\{(2,2),(2,3),(3,2),(3,3)\}$

Answer 2

Answer: A b 2.2]

Step-by-step explanation: