Question

If A={0,1} B={2,3,4} and C ={3,5} then verify A× (BuC)=(A×B)u(A×C)

Solution :

Answer 1

Step-by-step explanation:

Given :-

A = {0,1}

B = {2,3,4}

C = {3,5}

To find :-

Verify that A× (BUC)=(A×B)U(A×C) .

Solution :-

Given sets are :

A = {0,1}

B = {2,3,4}

C = {3,5}

I) A×(BUC):-

BUC = {2,3,4} U {3,5}

=> BUC = { 2,3,4,5}

Now,

A×(BUC) = {0,1} × { 2,3,4,5}

=> {(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)}

A×(BUC) ={(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)} -----------(1)

II) (A×B)U(A×C) :-

A×B = {0,1} × { 2,3,4}

=> {(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)}

and

A×C = {0,1} × {3,5}

=> {(0,3),(0,5)(1,3),(1,5)}

Now,

(A×B) U(A×C)

=> {(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)} U {(0,3),(0,5)(1,3),(1,5)}

=> {(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)} ------(2)

From (1)&(2)

A×(BUC) = (A×B) U(A×C)

Hence, Proved.

Anwer:-

A× (BUC)=(A×B)U(A×C)

Used formulae:-

→ AUB is the set of all elements either in A or in B or in both A and B.

→ A×B is the set of all order pairs in which first element belongs to A and second element belongs to B.