2025/2026 (WGU C959) MATH 2800 DISCRETE
MATHEMATICS I COMPREHENSIVE OA WITH
COMPLETE QUESTIONS AND CORRECT DETAILED
Page | 1
ANSWERS (EXPERT VERIFIED) FOR GUARANTEED
PASS|TOP RATED A+.
MATH 2800
Ace your WGU C959 (MATH 2800) Discrete Mathematics I
Comprehensive OA exam 2025/2026 with confidence. This resource
tests on foundational topics such as logic, set theory, functions,
algorithms, number theory, combinatorics, and graph theory. Mastery
of this assessment is crucial for success in computer science, data
structures, and advanced mathematical applications.
Exclusive or. ⊕ ....... ANSWER ...... One or the other,
but not both.
We can go to the park or the movies.
inclusive or is a: ....... ANSWER ...... disjunction
Order of operations in absence of parentheses. .......
ANSWER ...... 1. ¬ (not)
2. ∧ (and)
3. ∨ (or)
, the rule is that negation is applied first, then conjunction,
then disjunction:
Page | 2
truth table with three variables ....... ANSWER ...... see
pic
2^3 rows
proposition ....... ANSWER ...... p→q
Ex: If it is raining today, the game will be cancelled.
Converse: ....... ANSWER ...... q→p
If the game is cancelled, it is raining today.
Contrapositive ....... ANSWER ...... ¬q → ¬p
If the game is not cancelled, then it is not raining today.
Inverse: ....... ANSWER ...... ¬p → ¬q
, If it is not raining today, the game will not be cancelled.
Page | 3 biconditional ....... ANSWER ...... p↔q
true when P and Q have the same truth value.
see truth table pic.
free variable ....... ANSWER ...... ex.
P(x)
the variable is free to take any value in the domain
bound variable ....... ANSWER ...... ∀x P(x)
bound to a quantifier.
In the statement (∀x P(x)) ∧ Q(x), ....... ANSWER ......
the variable x in P(x) is bound
the variable x in Q(x) is free.
this statement is not a proposition cause of the free variable.
, summary of De Morgan's laws for quantified statements.
....... ANSWER ...... ¬∀x P(x) ≡ ∃x ¬P(x)
Page | 4
¬∃x P(x) ≡ ∀x ¬P(x)
using a truth table to establish the validity of an argument
....... ANSWER ...... see pic.
In order to use a truth table to establish the validity of an
argument, a truth table is constructed for all the hypotheses
and the conclusion.
A valid argument is a guarantee that the conclusion is true
whenever all of the hypotheses are true.
If when the hypotheses are true, the conclusion is not, then it
is invalid.
the argument works if every time the hypotheses (anything
above the line) are true, the conclusion is also true.
MATHEMATICS I COMPREHENSIVE OA WITH
COMPLETE QUESTIONS AND CORRECT DETAILED
Page | 1
ANSWERS (EXPERT VERIFIED) FOR GUARANTEED
PASS|TOP RATED A+.
MATH 2800
Ace your WGU C959 (MATH 2800) Discrete Mathematics I
Comprehensive OA exam 2025/2026 with confidence. This resource
tests on foundational topics such as logic, set theory, functions,
algorithms, number theory, combinatorics, and graph theory. Mastery
of this assessment is crucial for success in computer science, data
structures, and advanced mathematical applications.
Exclusive or. ⊕ ....... ANSWER ...... One or the other,
but not both.
We can go to the park or the movies.
inclusive or is a: ....... ANSWER ...... disjunction
Order of operations in absence of parentheses. .......
ANSWER ...... 1. ¬ (not)
2. ∧ (and)
3. ∨ (or)
, the rule is that negation is applied first, then conjunction,
then disjunction:
Page | 2
truth table with three variables ....... ANSWER ...... see
pic
2^3 rows
proposition ....... ANSWER ...... p→q
Ex: If it is raining today, the game will be cancelled.
Converse: ....... ANSWER ...... q→p
If the game is cancelled, it is raining today.
Contrapositive ....... ANSWER ...... ¬q → ¬p
If the game is not cancelled, then it is not raining today.
Inverse: ....... ANSWER ...... ¬p → ¬q
, If it is not raining today, the game will not be cancelled.
Page | 3 biconditional ....... ANSWER ...... p↔q
true when P and Q have the same truth value.
see truth table pic.
free variable ....... ANSWER ...... ex.
P(x)
the variable is free to take any value in the domain
bound variable ....... ANSWER ...... ∀x P(x)
bound to a quantifier.
In the statement (∀x P(x)) ∧ Q(x), ....... ANSWER ......
the variable x in P(x) is bound
the variable x in Q(x) is free.
this statement is not a proposition cause of the free variable.
, summary of De Morgan's laws for quantified statements.
....... ANSWER ...... ¬∀x P(x) ≡ ∃x ¬P(x)
Page | 4
¬∃x P(x) ≡ ∀x ¬P(x)
using a truth table to establish the validity of an argument
....... ANSWER ...... see pic.
In order to use a truth table to establish the validity of an
argument, a truth table is constructed for all the hypotheses
and the conclusion.
A valid argument is a guarantee that the conclusion is true
whenever all of the hypotheses are true.
If when the hypotheses are true, the conclusion is not, then it
is invalid.
the argument works if every time the hypotheses (anything
above the line) are true, the conclusion is also true.
