Which of the following statements are true ?

(i) {a} ⊂ {a, b, c}

(ii) {a} ⊂ {b, c, d, e}

(iii) Φ ⊂ {a, b, c}

(iv) Φ ∈ {a, b, c}

(v) 0 ∉ Φ

(vi) {1} ⊂ {0, 1}

(vii) Every subset of a finite set is finite.

(viii) Every subset of an infinite set is infinite.

(i) True
Reason — The element 'a' is present in the set {a, b, c}. Since {a} is a set containing an element from the second set, it is a proper subset.

(ii) False
Reason — For {a} to be a subset of {b, c, d, e}, the element 'a' must be present in the second set. Since it is not, the statement is false.

(iii) True
Reason — By definition, the empty set (Φ) is a subset of every set.

(iv) False
Reason — The symbol ∈ means "is an element of." Φ is a subset of {a, b, c}, not an element of it.

(v) True
Reason — The empty set (Φ) contains no elements at all. Therefore, it is correct to say that 0 is not an element of Φ.

(vi) True
Reason — The element 1 is present in the set {0, 1}, making {1} a proper subset.

(vii) True
Reason — A finite set has a specific number of elements. Any collection of elements taken from it will also have a specific, countable number of elements.

(viii) False
Reason — While an infinite set has endless elements, you can still pick a limited number of elements from it to form a subset. For example, {1, 2} is a finite subset of the infinite set of natural numbers {1, 2, 3, ….}.