Answer :

We know that when we write a set by defining its elements with a “common property”, we can say that the set is in set builder form.

(i) {3, 6, 9, 12}

⇒ 3, 6, 9, 12 are the multiples of 3 and they are less than 13.

∴ A={x: x is multiple of 3 & less than 13}

(ii) {2, 4, 8, 16, 32}

⇒ Here 2, 4, 8, 16, 32 are in the form of 2^{1}, 2^{2}, 2^{3}, 2^{4}, 2^{5}

Where 1, 2, 3, 4, 5 are the powers of 2 and power is less than 6.

∴ B = {x: x is a power of 2^{x} & x is less than 6}

(iii) {5, 25, 125, 625}

⇒ Here 5, 25, 125, 625 are in the form of 5^{1}, 5^{2}, 5^{3}, 5^{4}.

Where 1, 2, 3, 4 are the powers of 5 and power is less than 5.

∴ C = {x: x is a power of 5 & x is less than 5}

(iv){1, 4, 9, 16, 25 … 100}

⇒ Here 1, 4, 9 16, 25 … 100 are in the form of 1^{2}, 2^{2}, 3^{2}, 4^{2}, 5^{2} … 10^{2} where 1, 2, 3, 4, 5 … 10 are natural numbers and the given numbers are squares and not greater than 10.

∴ D = {x : x in square of natural number and not greater than 10}

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