State whether each of the following statement is true or false. Justify your answer.

Question

(i) {2, 3, 4, 5} and {3, 6} are disjoint sets.

(ii) {a, e, i, o, u } and {a, b, c, d} are disjoint sets.

(iii) {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.

(iv) {2, 6, 10} and {3, 7, 11} are disjoint sets.

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Salim Ahmed Kawsar · Answer 1 · Feb 05, 2023 15:29:48

(i) False As 3 ∈ {2, 3, 4, 5}, 3 ∈ {3, 6} ⇒ {2, 3, 4, 5} ∩ {3, 6} = {3}

(ii) False As a ∈ {a, e, i, o, u}, a ∈ {a, b, c, d} ⇒ {a, e, i, o, u } ∩ {a, b, c, d} = {a}

(iii) True As {2, 6, 10, 14} ∩ {3, 7, 11, 15} = Φ

(iv) True As {2, 6, 10} ∩ {3, 7, 11} = Φ

Salim Ahmed Kawsar · Answer 2 · Feb 05, 2023 15:29:48

(i) False

As 3 ∈ {2, 3, 4, 5}, 3 ∈ {3, 6}

⇒ {2, 3, 4, 5} ∩ {3, 6} = {3}

(ii) False

As a ∈ {a, e, i, o, u}, a ∈ {a, b, c, d}

⇒ {a, e, i, o, u } ∩ {a, b, c, d} = {a}

(iii) True

As {2, 6, 10, 14} ∩ {3, 7, 11, 15} = Φ

(iv) True

As {2, 6, 10} ∩ {3, 7, 11} = Φ

Salim Ahmed Kawsar · Answer 3 · Feb 05, 2023 15:29:48

(i) Let A = {2, 3, 4, 5} and B = {3, 6}

∴ A ∩ B = {3} ∴ A ∩ B ≠ φ

∴Given sets are disjoint sets.

(ii) Let A = {a, e, i, o, u} and B = {a, b, c, d}

A∩B = {a}.

Given sets are disjoint sets.

(iii) Given sets are A = {2, 6, 10, 14} and B = {3, 7, 11, 15}.

∴ A ∩ B =φ

(iv) Given sets are disjoint sets.

Let A = {2, 6, 10} and B = {3, 7, 11}

∴ A ∩ B = φ

∴ Given sets are disjoint sets.

3 Answers