Question 31 of 47intermediate🔍 AnalyzeShort Answer2 marks

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

(i)

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

Answer

False. The sets {2, 3, 4, 5} and {3, 6} are not disjoint sets because they have a common element 3. Two sets are called disjoint sets if their intersection is a null set (empty set). Here, {2, 3, 4, 5} ∩ {3, 6} = {3} ≠\neq φ. Hence, the statement is false.

(ii)

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

Answer

False. The sets {a, e, i, o, u} and {a, b, c, d} are not disjoint sets because they have a common element 'a'. Two sets are called disjoint sets if their intersection is a null set. Here, {a, e, i, o, u} ∩ {a, b, c, d} = {a} ≠\neq φ. Hence, the statement is false.

(iii)

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

Answer

True. The sets {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets because they have no common elements. Two sets are called disjoint sets if their intersection is a null set. Here, {2, 6, 10, 14} ∩ {3, 7, 11, 15} = φ. Hence, the statement is true.

(iv)

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

Answer

True. The sets {2, 6, 10} and {3, 7, 11} are disjoint sets because they have no common elements. Two sets are called disjoint sets if their intersection is a null set. Here, {2, 6, 10} ∩ {3, 7, 11} = φ. Hence, the statement is true.

Explanation

This question tests the understanding of disjoint sets from the Sets chapter. Two sets are said to be disjoint if their intersection is the empty set (null set), meaning they have no elements in common. To determine if sets are disjoint, we need to find their intersection and check if it equals φ. If A ∩ B = φ, the sets are disjoint; if A ∩ B ≠\neq φ, they are not disjoint.

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