Which of the following correctly represents the set of positive integers less than 6?
A{0, 1, 2, 3, 4, 5}
B{1, 2, 3, 4, 5}
C(1, 2, 3, 4, 5)
D{1, 2, 3, 4, 5, 6}
Positive integers start at 1 (not 0, since 0 is neither positive nor negative) and 'less than 6' excludes 6. The correct set is {1, 2, 3, 4, 5}. Option A includes 0 (not positive). Option C uses parentheses, which denote an ordered tuple, not a set. Option D includes 6, which is not less than 6.
Question 2 True / False
The sets {a, b, c} and {c, a, b} are different sets because the elements are in a different order.
TTrue
FFalse
Answer: False
Order does not matter in sets. Two sets are equal if and only if they contain exactly the same elements. {a, b, c} and {c, a, b} both contain a, b, and c and nothing else, so they are the same set.
Question 3 Short Answer
Write the set {3, 6, 9, 12, 15, 18} in set-builder notation.
Think about your answer, then reveal below.
Model answer: {x | x is a positive multiple of 3 and x ≤ 18}
Set-builder notation describes the set by a rule its elements satisfy. These are exactly the positive multiples of 3 up to 18. Equivalent formulations like {3n | n is a positive integer and n ≤ 6} are also correct. The key is that the rule must describe exactly the elements in the set — no more, no fewer.