Question

Express each of the following sets in set- builder notation (form):
(i)$\text{{3, 6, 9, 12, 15}}$
(ii)$\text{{2, 3, 5, 7, 11, 13 …. }}$
(iii)$\text{{1, 4, 9, 16, 25, 36}}$
(iv)$\text{{0, 2, 4, 6, 8, 10, 12, …. }}$
(v)$\text{{Monday, Tuesday, Wednesday}}$
(vi)$\text{{23, 25, 27, 29, … }}$
(vii)$\text{{1/3, 1/4, 1/5, 1/6, 1/7, 1/8}}$
(viii)$\text{{42, 49, 56, 63, 70, 77}}$

Answer 1

(i) $\text{{3, 6, 9, 12, 15}}$

It can be written as

=

$\text{{x: x is a natural number divisible by 3; x < 18}}$

(ii) $\text{{2, 3, 5, 7, 11, 13 ….}}$

It can be written as

=$\text{{x: x is a prime number}}$

(iii)$\text{{1, 4, 9, 16, 25, 36}}$

It can be written as

=$\text{{x: x is a perfect square natural number; x ≤ 36}}$

(iv)$\text{{0, 2, 4, 6, 8, 10, 12, ….}}$

It can be written as

=\text{{x: x is a whole number divisible by 2}}$

(v)\text{{Monday, Tuesday, Wednesday}}$

It can be written as

=$\text{{x: x is one of the first three days of the week}}$

(vi) $\text{{23, 25, 27, 29, …}}$

It can be written as

= $\text{{x: x is an odd natural number; x ≥ 23}}$

(vii) $\text{{1/3, 1/4, 1/5, 1/6, 1/7, 1/8}}$

It can be written as

= $\text{{x: x = 1/n when n is a natural number; 3 ≤ n ≤ 8}}$

(viii)$\text{{42, 49, 56, 63, 70, 77}}$

It can be written as

$=\text{{x: x is a natural number divisible by 7; 42 ≤ x ≤ 77}}$