State which of the following sets are disjoint

i. A = {2, 4, 6, 8}; B = {x : x is an even number < 10, }

ii. X = {1, 3, 5, 7, 9}, Y = {0, 2, 4, 6, 8, 10}

iii. P = {x : x is a prime < 15}

Q = {x : x is a multiple of 2 and x < 16}

iv. R = {a, b, c, d, e}, S = {d, e, a, b, c}

i. A = {2, 4, 6, 8}

B = {x : x is an even number < 10, x ∈}

B contains even natural numbers that are less than 10.

∴ B = {2, 4, 6, 8}

∴ A ∩ B = {2, 4, 6, 8} [elements that are present in both A and B]

∵ A ∩ B ≠ Φ

∴ A and B are not disjoint sets.

ii. X = {1, 3, 5, 7, 9}

Y = {0, 2, 4, 6, 8, 10}

∴ X ∩ Y = Φ [elements that are present in both X and Y]

∴ X and Y are disjoint sets.

iii. P = {x : x is a prime < 15}

P contains the prime numbers less than 15.

∴ P = {2, 3, 5, 7, 11, 13}

Q = {x : x is a multiple of 2 and x < 16}

Q contains the numbers that are less than 16 and multiple of 2.

∴ Q = {…-2, 0, 2, 4, 6, 8, 10, 12, 14}

∴ P ∩ Q = {2} [elements that are present in both P and Q]

∵ P ∩ Q ≠ Φ

∴ P and Q are not disjoint sets.

iv. R = {a, b, c, d, e}

S = {d, e, a, b, c}

R ∩ S = {d, e} [elements that are present in both R and S]

∵ R ∩ S ≠ Φ

∴ R and S are not disjoint sets.