Chapter 2 discrete math (sets, functions, sequences,
sums)Questions with complete solution 2026
1. definition of a set an unordered collection of distinct objects called
ele-ments or members of the set
2. roster method vs. set builder -roster method = represent sets with all elements
nota-tion listed between brackets, e.g., {1, 2, 3}
-set builder notation = stating property (or
properties) of members (image)
3. N {0, 1, 2, 3} = set of all natural numbers (or set
of all whole numbers in some textbooks)
4. Z {..., -2, -1, 0, 1, 2, ...} = set of all integers
5. Z+ the set of positive integers, {1, 2, 3, ...}
6. Q set of all rational numbers
7. R set of all real numbers
8. R+ set of all positive real numbers
9. C set of all complex numbers
10. when are two sets equal if and only if they contain the same elements
- order and number of times each element is listed don't
matter: {1, 3, 5} = {1, 3, 3, 5, 5, 5}
- {1,2} = {2,1} = {1,1,2} = {2,2,1,1}
11. empty set/null set a set with no elements
,Chapter 2 discrete math (sets, functions, sequences, sums)
12.singleton seta set with one element
13. universal set includes all elements in consideration, symbol
"U" in-cluded in Venn diagrams
14. subset and superset; proper subset - A is a subset of B, and B is a superset of A, if
every
element in A is also an element in B
-A †B, and B ‡A
-if A is a subset of B but B =/= A, then A is a
proper subset of B (A ‚B) (i.e., there is at least one
element in B that is not in A)
15. what two subsets do every the empty set and the set itself
non-empty set S have?
16. how to show two sets A and B equal show that A †B and B ‡A
17. cardinality definition if S is a finite set, then cardinality = size of the set
(aka,
the number of distinct elements in S)
-cardinality denoted as |S|
-|null set| = 0 b/c null set has no elements
18. power set of a set S; how many ele- power set = set of all subsets of S, and is
denoted P(S)
, ments in power set? -if a set has n elements, then its power set has
2^n elements
sums)Questions with complete solution 2026
1. definition of a set an unordered collection of distinct objects called
ele-ments or members of the set
2. roster method vs. set builder -roster method = represent sets with all elements
nota-tion listed between brackets, e.g., {1, 2, 3}
-set builder notation = stating property (or
properties) of members (image)
3. N {0, 1, 2, 3} = set of all natural numbers (or set
of all whole numbers in some textbooks)
4. Z {..., -2, -1, 0, 1, 2, ...} = set of all integers
5. Z+ the set of positive integers, {1, 2, 3, ...}
6. Q set of all rational numbers
7. R set of all real numbers
8. R+ set of all positive real numbers
9. C set of all complex numbers
10. when are two sets equal if and only if they contain the same elements
- order and number of times each element is listed don't
matter: {1, 3, 5} = {1, 3, 3, 5, 5, 5}
- {1,2} = {2,1} = {1,1,2} = {2,2,1,1}
11. empty set/null set a set with no elements
,Chapter 2 discrete math (sets, functions, sequences, sums)
12.singleton seta set with one element
13. universal set includes all elements in consideration, symbol
"U" in-cluded in Venn diagrams
14. subset and superset; proper subset - A is a subset of B, and B is a superset of A, if
every
element in A is also an element in B
-A †B, and B ‡A
-if A is a subset of B but B =/= A, then A is a
proper subset of B (A ‚B) (i.e., there is at least one
element in B that is not in A)
15. what two subsets do every the empty set and the set itself
non-empty set S have?
16. how to show two sets A and B equal show that A †B and B ‡A
17. cardinality definition if S is a finite set, then cardinality = size of the set
(aka,
the number of distinct elements in S)
-cardinality denoted as |S|
-|null set| = 0 b/c null set has no elements
18. power set of a set S; how many ele- power set = set of all subsets of S, and is
denoted P(S)
, ments in power set? -if a set has n elements, then its power set has
2^n elements
