State in each case, whether the given statement is true or false :

(i) If A is the set of all non-negative integers, then 0 ∈ A.

(ii) If B is the set of all consonants, then c ∈ B.

(iii) If C is the set of all prime numbers less than 80, then 57 ∈ C.

(iv) {x : x ∈ W, x + 5 = 5} is a singleton set.

(v) If D = {x : x ∈ W, x < 4}, then n(D) = 4.

(vi) {a, b, c, 1, 2, 3} is not a set.

(vii) {1, 2, 3, 1, 2, 3, 1, 2, 3,……………} is an infinite set.

(viii) 0 ∈ Φ.

(ix) {3, 5} ∈ (1, 3, 5, 7, 9).

(i) True
Reason — Non-negative integers include all natural numbers and zero (0, 1, 2, 3, ….). Therefore, 0 is an element of set A.

(ii) True
Reason — Consonants are all letters of the alphabet except for vowels (a, e, i, o, u). Since 'c' is not a vowel, it belongs to the set of consonants B.

(iii) False
Reason — A prime number has only two factors: 1 and itself. Since 57 is divisible by 3 (3 x 19 = 57), it is a composite number, not a prime number.

(iv) True
Reason — Solving x + 5 = 5 gives x = 0. Since 0 is a whole number (W), the set contains exactly one element: {0}. A set with one element is called a singleton set.

(v) True
Reason — The whole numbers (W) less than 4 are {0, 1, 2, 3}. Counting these elements gives a cardinal number n(D) = 4.

(vi) False
Reason — A set can contain any well-defined collection of distinct objects, including a mix of letters and numbers. Therefore, {a, b, c, 1, 2, 3} is a valid set.

(vii) False
Reason — In set theory, repeated elements are counted only once. The set {1, 2, 3, 1, 2, 3, ….} contains only the distinct elements {1, 2, 3}. Since it has a limited number of distinct elements, it is a finite set, not an infinite one.

(viii) False
Reason — The symbol Φ represents a null set, which by definition contains no elements at all. Therefore, 0 cannot be an element of Φ.

(ix) False
Reason — The notation {3, 5} represents a subset, not an element. The correct notation would be {3, 5} ⊂ {1, 3, 5, 7, 9} or 3, 5 ∈ {1, 3, 5, 7, 9}.