Which of the following collections is not a set?

The vowels in the English alphabet.

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All natural numbers which divide 42.

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Names of 10 most renowned actors.

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Names of rivers in India.

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Solution

The correct option is C
Names of 10 most renowned actors.

A set is a well-defined collection of objects.
a) Vowels in English alphabet are a, e, i, o, u. So, this is a set.
b) All natural numbers that divide 42 are 1, 2, 3, 6, 7, 14, 21, 42. This is also a set.

c) The collection of most renowned actors is not well-defined, because the criterion for selecting an actor as most renowned may vary from one person to another. So, this is not a set.

d) We may not be able to recollect immediately the names of all rivers, but the collection is well-defined i.e., given a river name, we can say whether it belongs to this set or not.

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Similar questions

Q. Examine whether the following statements are true or false:

(i) {a, b} \subset̸ {b, c, a}

(i i) {a, e} \subset {x : x

is a vowel in the English alphabet

}

(i i i) {1, 2, 3} \subset {1, 3, 5}

(i v) {a} \subset {a, b, c}

(v) {a} \in {a, b, c}

(v i) {x : x

is an even natural number less than

6} \subset {x : x

is a natural number which divides

36}

Examine whether the following statements are true or false:

(i) {a, b} ⊄ {b, c, a}

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

(iii) {1, 2, 3} ⊂{1, 3, 5}

(iv) {a} ⊂ {a. b, c}

(v) {a} ∈ (a, b, c)

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

Which of the following collections are sets ? Justify your answer :

(i) A collection of all natural numbers less than 50.

(ii) The collection of good hockey players in India.

(iii) The collection of all girls in your class.

Q. Let

V = {vowels in English alphabet}

. Write which of the following statements are true and which are false.

c \in V

The number assigned to each of the 26 alphabets namely A, B, C... Y and Z is 1, 2, 3... 25 and 26 respectively. A selection of certain alphabets is made such that the selection includes all the vowels and all those alphabets which have been assigned a prime number and a five-letter word using the alphabets from the selection is formed. Which of the following is definitely not a word that can be formed?

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