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)

Question

asked Oct 5, 2020 33.8k views

2 Answers

Hyarion · Answer 1 · 2020-10-12T05:55:51+0000

Answer:

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)
$(A\cap B)* (B\cap A)$

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

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

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