Answer:

(1)

A={ 1 }, B={ 1 }, & C={ 1 }

As, all the elements and the cardinal numbers of each set are equal

∴A=B=C, i.e, They are all equal sets

(2)

A={ 2 }, & B= { 2 }

Since, N[A]=n[B] and elements of A are same as that in B; THEREFORE, they are equal sets, A=B

(3)

(i) A = ɸ, [Empty set] ∵ there exists no such N, which is smaller than 1

(ii) B = { 0 }, [Single ton set] ∵ (0)²=0, therefore, there exist such value of x

(iii) C = { 2/5 }, [Singleton set] ∵ for x=2/5; 5x–2=0

(4)

(i) A = {1, 2, 3, 4, 5, 6, 7, 8, 9} [A finite set, ∵ n(A)=N]

(ii) B = {–2, –3, –4, –5,....} [An infinite set, ∵ n(B) = ∞]

(iii) A Finite set, As, there can be only a limited number of students according to the available seats in the school and not more than that.

(iv) A Finite set, As, the number of PEOPLE from village are countable, ALTHOUGH being a large number.

(v) A Finite set, The total number of Apparatuses are countable.

(vi) W = {0, 1, 2, 3, 4, 5,...}

[An Infinite set, ∵ n(W)=∞]

(vii) Q is an infinite set. As, there exists infinite number of rational numbers including all the integers(infinite), & x is of the form "p/q", q≠0, So, there can be made many such combinations of rational numbers.