Q. 15.0( 1 Vote )

# Find A ∪ B and A ∩ B for the following sets.

i. A = {0, 1, 2, 4, 6} and B = {−3, −1, 0, 2, 4, 5}

ii. A = {2, 4, 6, 8} and B = Φ

iii. and B = {x : x is a prime number less than 11}

iv. and

Answer :

i. A = {0, 1, 2, 4, 6}

B = {-3, -1, 0, 2, 4, 5}

∴ A ∪ B = {-3, -1, 0, 1, 2, 4, 5, 6} [elements that are present in either A or B]

∴ A ∩ B = {0, 2, 4} [elements that are present in both A and B]

ii. A = {2, 4, 6, 8} and B = Φ

∴ A ∪ B = {2, 4, 6, 8} [elements that are present in either A or B]

∴ A ∩ B = Φ [elements that are present in both A and B]

iii. A = {x : x ∈ N, x ≤ 5}

∴ A contains the Natural numbers that are less than or equal to 5.

∴ A = {1, 2, 3, 4, 5}

B = {x : x is a prime number less than 11}

Prime numbers less than 11 are : 2, 3, 5, 7

∴ B = {2, 3, 5, 7}

∴ A ∪ B = {1, 2, 3, 4, 5, 7} [elements that are present in either A or B]

∴ A ∩ B = {2, 3, 5} [elements that are present in both A and B]

iv. A = {x : x ∈ N, 2 < x ≤ 7}

∴ A contains the Natural numbers that are greater than 2 and less than equal to 7

∴ A = {3, 4, 5, 6, 7}

B = {x : x ∈ W, 0≤ x ≤ 6}

∴ B contains the whole numbers that are greater than or equal to 0 and less than or equal to 6.

∴ B = {0, 1, 2, 3, 4, 5, 6}

∴ A ∪ B = {0, 1, 2, 3, 4, 5, 6, 7} [elements that are present in either A or B]

∴ A ∩ B = {3, 4, 5, 6} [elements that are present in both A and B]

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