Question

Write the following sets in the set-builder form: (i) (3, 6, 9, 12) (ii) {2, 4, 8, 16, 32} (iii) {5, 25, 125, 625} (iv) {2, 4, 6 …} (v) {1, 4, 9 … 100}

Answer 1

(i)

The given set is A={ 3,6,9,12 }.

Since, the elements in the given set are the multiples of 3, so the set builder form of the given set is,

A={ x:x=3n, n∈N and 1≤n≤4 }

(ii)

The given set is B={ 2,4,8,16,32 }

Since, the elements in the given set are the multiple powers of 2, so, the set builder form of the given set is,

B={ x:x= 2 n , n∈N and 1≤n≤5 }

(iii)

The given set is C={ 5,25,125,625 }

Since, the elements in the given set are the multiple powers of 5, so, the set builder form of the given set is,

C={ x:x= 5 n , n∈N and 1≤n≤4 }

(iv)

The given set is D={ 2,4,6,… }

Since the elements in the given set are even numbers, so, the set builder form of the given set is,

D={ x:x is an even natural number }

(v)

The given set is E={ 1,4,9,…,100 }

Since the elements in the given set are the squares of the natural numbers, so, the set builder form of the given set is,

E={ x:x= n 2 , n∈N and 1≤n≤10 }