State whether the following sets are empty, finite or infinite sets. In case of (non-empty) finite sets, mention the cardinal number.

(i) {all colours of a rainbow}

(ii) {x | x is a prime number between 7 and 11}

(iii) {x | x is a digit in the numeral 550131527}

(iv) {x | x is a letter in the word 'SUFFICIENT'}

(v) {x | x is a vowel in the word MATHEMATICS}

(vi) {x : x is an even whole number and x ≤ 20}

(vii) {x : x ∈ I and -2 ≤ x < 5}

(viii) {x : x is a prime number less than 25}

(ix) {x : x is a prime factor of 180}

(x) {x : x ∈ N and x is a composite number < 12}

(i) The colours of a rainbow are Violet, Indigo, Blue, Green, Yellow, Orange and Red.

{all colours of a rainbow} = {Violet, Indigo, Blue, Green, Yellow, Orange, Red}

It has 7 elements.

Hence, it is a finite set with cardinal number 7.

(ii) There is no prime number between 7 and 11 (since 8, 9 and 10 are not prime).

{x | x is a prime number between 7 and 11} = { }

Hence, it is an empty set.

(iii) The digits in the numeral 550131527 are 5, 5, 0, 1, 3, 1, 5, 2, 7. Writing each digit only once, we get 5, 0, 1, 3, 2, 7.

{x | x is a digit in the numeral 550131527} = {5, 0, 1, 3, 2, 7}

It has 6 elements.

Hence, it is a finite set with cardinal number 6.

(iv) The letters in the word 'SUFFICIENT' are S, U, F, F, I, C, I, E, N, T. Writing each letter only once, we get S, U, F, I, C, E, N, T.

{x | x is a letter in the word 'SUFFICIENT'} = {S, U, F, I, C, E, N, T}

It has 8 elements.

Hence, it is a finite set with cardinal number 8.

(v) The letters in the word MATHEMATICS are M, A, T, H, E, M, A, T, I, C, S. The vowels among these are A, E, A, I. Writing each letter only once, we get A, E, I.

{x | x is a vowel in the word MATHEMATICS} = {A, E, I}

It has 3 elements.

Hence, it is a finite set with cardinal number 3.

(vi) The even whole numbers ≤ 20 are 0, 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20.

{x : x is an even whole number and x ≤ 20} = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20}

It has 11 elements.

Hence, it is a finite set with cardinal number 11.

(vii) The integers x such that -2 ≤ x < 5 are -2, -1, 0, 1, 2, 3 and 4.

{x : x ∈ I and -2 ≤ x < 5} = {-2, -1, 0, 1, 2, 3, 4}

It has 7 elements.

Hence, it is a finite set with cardinal number 7.

(viii) The prime numbers less than 25 are 2, 3, 5, 7, 11, 13, 17, 19 and 23.

{x : x is a prime number less than 25} = {2, 3, 5, 7, 11, 13, 17, 19, 23}

It has 9 elements.

Hence, it is a finite set with cardinal number 9.

(ix) 180 = 2 × 2 × 3 × 3 × 5 = 2² × 3² × 5

So, the prime factors of 180 are 2, 3 and 5.

{x : x is a prime factor of 180} = {2, 3, 5}

It has 3 elements.

Hence, it is a finite set with cardinal number 3.

(x) The composite natural numbers less than 12 are 4, 6, 8, 9 and 10.

{x : x ∈ N and x is a composite number < 12} = {4, 6, 8, 9, 10}

It has 5 elements.

Hence, it is a finite set with cardinal number 5.