Question

Find B, when: A={3,4} A intersection B={3} AUB={1,2,3,4}

Answer 1

A = { 3, 4 }; A ∩ B = {3}; A ∪ B={1,2,3,4}

So, B = {1,2,3}

From the first condition we got to know that B has alteast 3 as its element and from the second condition we get to know that the set B has 1 , 2, & 3 as its 3 elements satisfying both conditions simultaneously.

Answer 2

Given,

• A = { 3 , 4 }

• A∩B = { 3 }

• A∪B = { 1 , 2 , 3 , 4 }

We know the equation,

B = A∩B + A∪B - A

Applying the values to the equation,

B = { 3 } + { 1 , 2 , 3 , 4 } - { 3 , 4 }

B = { 1 , 2 , 3 }

$\boxed{B = \{1,2,3\}}$