WGU C960 (MATH 2810) Discrete
Mathematics II OA EXAM STUDY GUIDE
2025/2026 COMPLETE QUESTIONS WITH
VERIFIED CORRECT ANSWERS ||
100% GUARANTEED PASS
<LATEST VERSION>
1. The primary resources to optimize are - ANSWER ✔ time complexity, the
time the algorithm requires to run, and space complexity, the amount of
memory used.
2. time depends on the - ANSWER ✔ speed of the processing unit, the number
of calculations that need to be performed, the number of conditions that need
to be evaluated, or the number of iterations to be completed by the loops
3. the values of all variables, including the values of the input variables and all
other values that will be computed, need to be - ANSWER ✔ stored
somewhere in the memory of the system—in the RAM, hard drive, or
external devices
4. each algorithm uses - ANSWER ✔ assignments, conditional statements, and
loops, and performs a variety of operations, such as addition and
multiplication
,5. operations such as addition, multiplication, comparison that one would find
in a single line of pseudocode, are referred to as - ANSWER ✔ atomic
operations, because they cannot be split any further; a computer would
evaluate each in one step
6. The bijection rule says that if there is a bijection from one set to another then
the two sets have the same - ANSWER ✔ cardinality
7. Let S and T be two finite sets. If there is a bijection from S to T, then: -
ANSWER ✔ |S| = |T|
8. r-Permutation: - ANSWER ✔ A sequence of r items chosen from n total
items in which the order of the items matters
9. An r-permutation is denoted and calculated as - ANSWER ✔ P(n,r) = n! /
(n − r)!
10.Permutation: - ANSWER ✔ A sequence of n items in which the order of the
items matters and every item in a set is included exactly once
11.A permutation is denoted and calculated as - ANSWER ✔ P(n,n) = n!
12.r-Subset (or r-combination): - ANSWER ✔ A sequence of r items chosen
from n total items in which the order of the items does not matter
13.An r-combination is denoted and calculated as - ANSWER ✔ C(n,r) =
(nr) = n! / r!(n−r)!
,14.Sets are collection of - ANSWER ✔ distinct items
15.A multiset is a collection that can have - ANSWER ✔ multiple instances of
the same kind of item
16.The number of ways to place n indistinguishable balls into m distinguishable
bins is - ANSWER ✔ (n + m - 1) / (m - 1)
17.The Pigeonhole Principle
If a function f has a domain of size at least n+1 and a target of size at most n,
where n is a positive integer, then there are - ANSWER ✔ two elements in
the domain that map to the same element in the target (i.e., the function is
not one-to-one)
18.Contrapositive of the generalized pigeonhole principle
Suppose that a function maps a set of n elements to a target set with k
elements, where n and k are positive integers. In order to guarantee that there
is an element y in the target to which f maps at least b items, then n must be
- ANSWER ✔ at least k(b - 1) + 1.
19.Filling positions left to right?
(keywords: password, code, callsign, string) - ANSWER ✔ PRODUCT
RULE
Multiply choices for each position
Repetition allowed unless stated otherwise
if the number of choices for each position is the sameyou can raise it to a
power instead.
, 20.Choosing a group where order does NOT matter
(keywords: choose, select, committee, hand) - ANSWER ✔
COMBINATION
(n choose k)
Arranging people/items and order DOES NOT matter
(keywords: line up, arrange, seat, rank)
21.Identical objects + categories - ANSWER ✔ MULTISET counting
22.The problem says "either ... or ..."? - ANSWER ✔ SUM RULE
Solve each case
Add results
In Euclid's algorithm, we use a repeated application of Division algorithm.
Apply Euclid's algorithm to a=178 and b=20, we get
178=20×8+1820=18×1+218=2×9+0
Here the last non-zero remainder in the Euclid's algorithm is equal to 2.
Explanation:
The last non-zero remainder in the euclidean algorithm gives the GCD of
two numbers
The greatest common divisor (GCD) of 178 and 20 is equal to
GCD(178,20)=2.
23.Pre-Assessment: Recursion and Induction - Induction Methods
Mathematics II OA EXAM STUDY GUIDE
2025/2026 COMPLETE QUESTIONS WITH
VERIFIED CORRECT ANSWERS ||
100% GUARANTEED PASS
<LATEST VERSION>
1. The primary resources to optimize are - ANSWER ✔ time complexity, the
time the algorithm requires to run, and space complexity, the amount of
memory used.
2. time depends on the - ANSWER ✔ speed of the processing unit, the number
of calculations that need to be performed, the number of conditions that need
to be evaluated, or the number of iterations to be completed by the loops
3. the values of all variables, including the values of the input variables and all
other values that will be computed, need to be - ANSWER ✔ stored
somewhere in the memory of the system—in the RAM, hard drive, or
external devices
4. each algorithm uses - ANSWER ✔ assignments, conditional statements, and
loops, and performs a variety of operations, such as addition and
multiplication
,5. operations such as addition, multiplication, comparison that one would find
in a single line of pseudocode, are referred to as - ANSWER ✔ atomic
operations, because they cannot be split any further; a computer would
evaluate each in one step
6. The bijection rule says that if there is a bijection from one set to another then
the two sets have the same - ANSWER ✔ cardinality
7. Let S and T be two finite sets. If there is a bijection from S to T, then: -
ANSWER ✔ |S| = |T|
8. r-Permutation: - ANSWER ✔ A sequence of r items chosen from n total
items in which the order of the items matters
9. An r-permutation is denoted and calculated as - ANSWER ✔ P(n,r) = n! /
(n − r)!
10.Permutation: - ANSWER ✔ A sequence of n items in which the order of the
items matters and every item in a set is included exactly once
11.A permutation is denoted and calculated as - ANSWER ✔ P(n,n) = n!
12.r-Subset (or r-combination): - ANSWER ✔ A sequence of r items chosen
from n total items in which the order of the items does not matter
13.An r-combination is denoted and calculated as - ANSWER ✔ C(n,r) =
(nr) = n! / r!(n−r)!
,14.Sets are collection of - ANSWER ✔ distinct items
15.A multiset is a collection that can have - ANSWER ✔ multiple instances of
the same kind of item
16.The number of ways to place n indistinguishable balls into m distinguishable
bins is - ANSWER ✔ (n + m - 1) / (m - 1)
17.The Pigeonhole Principle
If a function f has a domain of size at least n+1 and a target of size at most n,
where n is a positive integer, then there are - ANSWER ✔ two elements in
the domain that map to the same element in the target (i.e., the function is
not one-to-one)
18.Contrapositive of the generalized pigeonhole principle
Suppose that a function maps a set of n elements to a target set with k
elements, where n and k are positive integers. In order to guarantee that there
is an element y in the target to which f maps at least b items, then n must be
- ANSWER ✔ at least k(b - 1) + 1.
19.Filling positions left to right?
(keywords: password, code, callsign, string) - ANSWER ✔ PRODUCT
RULE
Multiply choices for each position
Repetition allowed unless stated otherwise
if the number of choices for each position is the sameyou can raise it to a
power instead.
, 20.Choosing a group where order does NOT matter
(keywords: choose, select, committee, hand) - ANSWER ✔
COMBINATION
(n choose k)
Arranging people/items and order DOES NOT matter
(keywords: line up, arrange, seat, rank)
21.Identical objects + categories - ANSWER ✔ MULTISET counting
22.The problem says "either ... or ..."? - ANSWER ✔ SUM RULE
Solve each case
Add results
In Euclid's algorithm, we use a repeated application of Division algorithm.
Apply Euclid's algorithm to a=178 and b=20, we get
178=20×8+1820=18×1+218=2×9+0
Here the last non-zero remainder in the Euclid's algorithm is equal to 2.
Explanation:
The last non-zero remainder in the euclidean algorithm gives the GCD of
two numbers
The greatest common divisor (GCD) of 178 and 20 is equal to
GCD(178,20)=2.
23.Pre-Assessment: Recursion and Induction - Induction Methods
