💡 Practical Examples
Example 1: Vowels V = {a, e, i, o, u}.
Result: e ∈ V but b ∉ V.
Example 2: Letters in "SUCCESS" S = {S, U, C, E}.
Result: n(S) = 4 (duplicates removed).
Click the button below each question to reveal the explanation.
1. Is "The set of best football players" a set?
Answer: No. "Best" is a matter of opinion (subjective), making it not well-defined.
2. Is "The set of even numbers less than 10" well-defined?
Answer: Yes. The rule is clear and measurable: {2, 4, 6, 8}.
3. List elements of set L: {letters in "BANANA"}
Answer: {B, A, N}. In set notation, we ignore repeated letters.
4. Find n(A) if A = {10, 20, 30, 40, 50}.
Answer: 5. There are five distinct elements in the set.
5. Use the correct symbol: 7 __ {2, 4, 6, 8}
Answer: ∉. 7 is not a member of the set of even numbers.
6. Use the correct symbol: a __ {a, b, c}
Answer: ∈. 'a' is explicitly listed as a member.
7. Does the order of elements matter in {1, 2, 3}?
Answer: No. {1, 2, 3} is identical to {3, 2, 1}.
8. What is the cardinality of an empty set?
Answer: 0. An empty set contains no elements.
9. Write in symbols: "Red is an element of set C".
Answer: Red ∈ C.
10. Is 0 ∈ ∅ true or false?
Answer: False. The empty set contains absolutely nothing.
11. List elements: {Natural numbers less than 4}.
Answer: {1, 2, 3}. Natural numbers start at 1.
12. Find n(A) for A = {0}.
Answer: 1. Zero is a valid element, so the set is not empty.
13. Define "Cardinality".
Answer: The count of unique elements in a set.
14. If B = {x, {y, z}}, is y ∈ B?
Answer: No. 'y' is inside a subset. The elements of B are 'x' and the set '{y, z}'.
15. Is "Beautiful cities" a set?
Answer: No. Beauty is subjective.
16. List elements: {Days of the week starting with S}.
Answer: {Saturday, Sunday}.
17. Is {1, 2} = {1, 1, 2, 2}?
Answer: Yes. Repetitions do not create new elements in a set.
18. Symbol for "not a member of"?
Answer: ∉.
19. List elements: {Factors of 4}.
Answer: {1, 2, 4}.
20. What is another name for a member of a set?
Answer: An element.