Question

If A = { 1 , 2 , 3 } , B = { 3 , 4 } and C = { 4 , 5 , 6 } then ( A X B ) ∩ ( B X C ) is equal to

a) ( 1 , 4 ) b) ( 3 , 4 ) c) ( 4 , 4 )​

Answer 1

Answer:

b) (3, 4)

Step-by-step explanation:

Given,

A = {1 , 2 , 3}

B = {3 , 4}

C = {4 , 5 , 6}

To Find :-

Value of :-

(A × B) ∩ (B × C)

Solution :-

Finding value of {A × B} :-

= {1 , 2 , 3} × {3 , 4}

We need to consider each and every element of 'A' with each and every element of 'B' as a set :-

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

∴ {A × B } = { (1 , 3) , (1 , 4) , (2 , 3) , (2 , 4) , (3 , 3) , (3 , 4) }

Finding value of {B × C} :-

= {3 , 4} × {4 , 5 , 6}

We need to consider each and every element of 'B' with each and every element of 'C' as a set :-

= { (3 , 4), (3 , 5) , (3 , 6) , (4 , 4) , (4 , 5) , (4 , 6) }

∴ (B × C) =  { (3 , 4), (3 , 5) , (3 , 6) , (4 , 4) , (4 , 5) , (4 , 6) }

(A × B) ∩ (B × C)

= { (1 , 3) , (1 , 4) , (2 , 3) , (2 , 4) , (3 , 3) , (3 , 4) } ∩ { (3 , 4), (3 , 5) , (3 , 6) , (4 , 4) , (4 , 5) , (4 , 6) }

[ ∴ WE need to write the common term in both the sets ]

= {3 , 4}

(A × B) ∩ (B × C) = {3 , 4}

Option 'b'