Question

State which pairs of sets are disjoint or overlapping?
(i) A = {f, i, a, s} and B = {a, n, f, h, s)

Answer 1

(i) A = {f, i, a, s}

B = {a, n, f, h, s} A ∩ B

= {f, i, a, s} ∩ {a, n,f h, s}

= {f, a, s} Since A ∩ B ≠ ϕ ,

A and B are overlapping sets.

(ii) C = {3, 5, 7, 11, ...} D = {2}

C ∩ D = {3, 5, 7, 11, ... } ∩ {2}

= { } Since C ∩ D = Ø,

C and D are disjoint sets.

(iii) E = {1, 2, 3, 4, 6, 8, 12, 24}

F = {3, 6, 9, 12, 15, 18, 21, 24, 27} E ∩ F

= {1, 2, 3, 4, 6, 8, 12, 24} ∩ {3, 6, 9, 12, 15, 18, 21, 24, 27} = {3, 6, 12, 24} Since E ∩ F ≠ ϕ, E and F are overlapping set .

Answer 2

$\huge\tt\underline\red{Answer:-}$

(i) A = {f, i, a, s}

B = {a, n, f, h, s} A ∩ B

= {f, i, a, s} ∩ {a, n,f h, s}

= {f, a, s} Since A ∩ B ≠ ϕ ,

A and B are overlapping sets.

(ii) C = {3, 5, 7, 11, ...} D = {2}

C ∩ D = {3, 5, 7, 11, ... } ∩ {2}

= { } Since C ∩ D = Ø,

C and D are disjoint sets.

(iii) E = {1, 2, 3, 4, 6, 8, 12, 24}

F = {3, 6, 9, 12, 15, 18, 21, 24, 27} E ∩ F

= {1, 2, 3, 4, 6, 8, 12, 24} ∩ {3, 6, 9, 12, 15, 18, 21, 24, 27} = {3, 6, 12, 24} Since E ∩ F ≠ ϕ, E and F are overlapping set .