Question 13 of 47beginner💡 UnderstandShort Answer2 marks

Examine whether the following statements are true or false:

(i)

{a, b} ⊄ {b, c, a}

Answer

False. The statement claims that {a, b} is not a subset of {b, c, a}. However, the elements 'a' and 'b' are both present in the set {b, c, a}. Therefore, {a, b} is a subset of {b, c, a}, making the given statement false.

(ii)

{a, e} ⊂ {x : x is a vowel in the English alphabet}

Answer

True. The set of vowels in the English alphabet is {a, e, i, o, u}. The elements 'a' and 'e' in the first set are both present in this set of vowels. Thus, {a, e} is a subset of the set of vowels.

(iii)

{1, 2, 3} ⊂ {1, 3, 5}

Answer

False. The element '2' is present in the set {1, 2, 3} but is not present in the set {1, 3, 5}. Since not every element of the first set is in the second set, {1, 2, 3} is not a subset of {1, 3, 5}.

(iv)

{a} ⊂ {a, b, c}

Answer

True. The element 'a' in the set {a} is also present in the set {a, b, c}. Therefore, {a} is a subset of {a, b, c}.

(v)

{a} ∈ {a, b, c}

Answer

False. The symbol '∈' represents 'is an element of'. The elements of the set {a, b, c} are 'a', 'b', and 'c'. The set {a} is not an element of {a, b, c}; rather, 'a' is the element.

(vi)

{x : x is an even natural number less than 6} ⊂ {x : x is a natural number which divides 36}

Answer

True. The set of even natural numbers less than 6 is {2, 4}. The set of natural numbers which divide 36 is {1, 2, 3, 4, 6, 9, 12, 18, 36}. Since elements 2 and 4 are present in the second set, the first set is a subset of the second.

Explanation

This question tests the understanding of subsets and the distinction between the symbols '⊂' (is a subset of) and '∈' (belongs to). A set A is a subset of set B if every element of A is also an element of B. In part (i), the statement is false because the set is indeed a subset. In part (iii), the presence of element '2' in the first set but not the second makes it a false statement. Part (v) highlights a common error where students confuse a set containing an element with the element itself; {a} is a set, not an element of {a, b, c}. Part (vi) requires listing the elements of both sets to verify the subset relationship.

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