Question

1 2 10. (i) Given A = 4 5 and B= GO 2 3 5 6 Find AB and BA 1 0 (ii) If A = 2 1 and B = then 2 3 4 2 Prove that AB +BA if 1 4 A= 4 1 and B= 5 7 4 5​

Answer 1

Answer:

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. Mark me as Brainlist