Which of the following sets is equal to {3, 1, 2, 1}?
A{1, 2, 3}
B{3, 1, 2, 1, 1}
C{1, 1, 2, 3}
DNone — the sets differ because the orders differ
Sets contain only distinct elements and are order-independent. {3,1,2,1} has distinct elements 1, 2, and 3, which equals {1,2,3}. The repeated 1 and the listing order are irrelevant to set identity.
Question 2 True / False
The notation (3, 5) and the notation {3, 5} represent the same mathematical object.
TTrue
FFalse
Answer: False
(3,5) is an ordered pair (or an open interval on the real line), where position matters. {3,5} is a set, where order does not matter and {3,5} = {5,3}. These are distinct mathematical objects with different definitions and uses.
Question 3 Short Answer
Translate the set {2, 4, 6, 8, 10} into set-builder notation.
Think about your answer, then reveal below.
Model answer: {x | x is a positive even integer and x ≤ 10}
Set-builder notation {x | P(x)} names a variable and states the condition all members satisfy. This set contains exactly the positive even integers up to 10. Equivalent formulations such as {x ∈ ℤ | x = 2n, 1 ≤ n ≤ 5} are also correct — multiple phrasings can describe the same set.