Question 28 of 47beginner🔧 ApplyShort Answer4 marks
Write the following sets in the set-builder form:
(i)
{3, 6, 9, 12}
Answer
{x : x = 3n, where n ∈ N and 1 n 4}
(ii)
{2, 4, 8, 16, 32}
Answer
{x : x = 2ⁿ, where n ∈ N and 1 n 5}
(iii)
{5, 25, 125, 625}
Answer
{x : x = 5ⁿ, where n ∈ N and 1 n 4}
(iv)
{2, 4, 6, ...}
Answer
{x : x is an even natural number}
(v)
{1, 4, 9, ..., 100}
Answer
{x : x = n², where n ∈ N and 1 n 10}
Explanation
To convert from roster form to set-builder form, we identify the pattern or property that defines all elements of the set. For finite sets, we specify the range of values; for infinite sets, we describe the general property that all elements satisfy.