Question

consider the set A={2,3,5,7}and B={1,2,3,4,6,12} find AnB find A-B ,B-A and hence show that (AnB)u(A-B)u(B-A) =AuB​

Answer 1

SOLUTION

GIVEN

Consider the set

• A = { 2 , 3 , 5 , 7 }

• B = { 1 , 2 , 3 , 4 , 6 , 12 }

TO DETERMINE

• A ∩ B

• A - B

• B - A

• To Prove :

( A ∩ B ) ∪ ( A - B ) ∪ ( B - A ) = A ∪ B

EVALUATION

Here the given two sets are

A = { 2 , 3 , 5 , 7 }

B = { 1 , 2 , 3 , 4 , 6 , 12 }

∴ A ∩ B = { 2, 3 }

∴ A - B = { 5, 7 }

∴ B - A = { 1 , 4, 6, 12 }

Now

A ∪ B = { 1 , 2 , 3 , 4 , 5, 6, 7 , 12 }

Now

( A ∩ B ) ∪ ( A - B ) = { 2 , 3 , 5 , 7 }

∴ ( A ∩ B ) ∪ ( A - B ) ∪ ( B - A )

= { 1 , 2 , 3 , 4 , 5, 6, 7 , 12 }

LHS

= ( A ∩ B ) ∪ ( A - B ) ∪ ( B - A )

= { 1 , 2 , 3 , 4 , 5, 6, 7 , 12 }

RHS

= A ∪ B

= { 1 , 2 , 3 , 4 , 5, 6, 7 , 12 }

∴ LHS = RHS

Hence proved

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ If A and B are two sets

then A-B =B-A if

https://brainly.in/question/28848928

2. Using venn diagram verify :

An(BuC) =(AnB) u (AnC)

https://brainly.in/question/12700100