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Standard VIII

Mathematics

Definition of Sets

Which of the ...

Question

Which of the following collection 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.

Option A → Vowels in English alphabet are a, e, i, o, u. This collection is well defined So, this is a set.

Option B → All natural numbers that divide 42 are 1, 2, 3, 6, 7, 14, 21, 42. This collection is well defined. This is also a set.

Option C → This collection is not well-defined, because the criterion for selecting an actor as most renowned may vary from a person to other. So, option C does not represent a set.

Option D → It is possible to list all the rivers of India so, the collection is well-defined. This is a set.

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Similar questions

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. 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}

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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