Let U = {x : x is a positive integer less than 50}, A = {x : x is divisible by 4} and B = {x : x leaves a remainder 2 when divided by 14}.

i. List the elements of U, A and B

ii. Find A ∪ B, A ∩ B, n(A ∪ B), n(A ∩ B)

i. U = {x : x is a positive integer less than 50}

U contains all the positive integers that are less than 50.

∴ U = {1, 2, 3, 4 ……… 49}

A = {x : x is divisible by 4}

A contains all the members of U that are divisible by 4. [∵U is universal set]

Numbers present in U that are divisible by 4 are : 4, 8, 12 …… 48.

∴ A = {4, 8, 12 …… 48}

B = {x : x leaves a remainder 2 when divided by 14}

B contains all the elements of U that leaves a remainder 2 when divided by 14.

Such numbers present in U are : 16, 30, 44

∴ B = {16, 30, 44}

ii. A = {4, 8, 12 …… 48}

B = {16, 30, 44}

∴ A ∪ B = {4, 8, 12, 16, 20, 24, 28, 30, 32, 36, 40, 44, 48} [elements that are present in either A or B]

∴ A ∩ B = {16, 44} [elements that are present in both A and B]

∴ n(A ∪ B) = 13 [no. of elements in A ∪ B]

∴ n(A ∩ B) = 2 [no. of elements in A ∩ B]