Mathematics: 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)

idkStep-by-step explanation:...

let a = {1,2,3} and b = {2,3,4}. determine the

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07.01.2022

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

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

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

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

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