age 1 of 56
WGU D420 Discrete Math Logic ACTUAL EXAM STUDY
GUIDE 2025/2026 ACCURATE QUESTIONS AND
VERIFIED CORRECT SOLUTIONS WITH RATIONALES ||
100% GUARANTEED PASS <LATEST VERSION>
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)
,age 2 of 56
the rule is that negation is applied first, then conjunction, then
disjunction:
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
,age 3 of 56
If it is not raining today, the game will not be cancelled.
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
, age 4 of 56
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)
¬∃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.
WGU D420 Discrete Math Logic ACTUAL EXAM STUDY
GUIDE 2025/2026 ACCURATE QUESTIONS AND
VERIFIED CORRECT SOLUTIONS WITH RATIONALES ||
100% GUARANTEED PASS <LATEST VERSION>
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)
,age 2 of 56
the rule is that negation is applied first, then conjunction, then
disjunction:
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
,age 3 of 56
If it is not raining today, the game will not be cancelled.
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
, age 4 of 56
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)
¬∃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.
