WGU D420 Discrete Math Logic ACTUAL EXAM
STUDY GUIDE 2025/2026 ACCURATE QUESTIONS
AND VERIFIED CORRECT SOLUTIONS WITH
RATIONALES || 100% GUARANTEED PASS
<LATEST VERSION>
1. Commutative Laws - ANSWER ✓ p ∨ q ≡ q ∨ p
p∧q≡q∧p
2. Associative Laws - ANSWER ✓ (p ∨ q) ∨ r ≡ p ∨ (q ∨ r)
(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)
3. Distributive Laws - ANSWER ✓ p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)
p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)
4. Identity Laws - ANSWER ✓ p ∧ 1 ≡ p
p∨0≡p
5. Negation Laws - ANSWER ✓ p ∨ ¬p ≡ 1
p ∧ ¬p ≡ 0
6. Idempotent Laws - ANSWER ✓ p ∨ p ≡ p
p∧p≡p
7. Null Laws - ANSWER ✓ p ∧ 0 ≡ 0
p∨1≡1
8. Absorption Laws - ANSWER ✓ p ∨ (p ∧ q) ≡ p
p ∧ (p ∨ q) ≡ p
9. DeMorgan's Laws - ANSWER ✓ ¬(p ∨ q) ≡ ¬p ∧ ¬q
¬(p ∧ q) ≡ ¬p ∨ ¬q
,10.Involution Law - ANSWER ✓ ¬(¬p) ≡ p
11.Conditional Equivalence - ANSWER ✓ p → q ≡ ¬p ∨ q
12.Contrapositive - ANSWER ✓ p → q ≡ ¬p → ¬q
13.Chain Rule - ANSWER ✓ (p → q) ∧ (q → r) ≡ (p → r)
14.Exclusive or. ⊕ - ANSWER ✓ One or the other, but not both.
We can go to the park or the movies.
15.inclusive or is a: - ANSWER ✓ disjunction
16.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:
17.truth table with three variables - ANSWER ✓ see pic
2^3 rows
18.proposition - ANSWER ✓ p → q
Ex: If it is raining today, the game will be cancelled.
19.Converse: - ANSWER ✓ q → p
If the game is cancelled, it is raining today.
20.Contrapositive - ANSWER ✓ ¬q → ¬p
If the game is not cancelled, then it is not raining today.
21.Inverse: - ANSWER ✓ ¬p → ¬q
If it is not raining today, the game will not be cancelled.
22.biconditional - ANSWER ✓ p ↔ q
, true when P and Q have the same truth value.
see truth table pic.
23.free variable - ANSWER ✓ ex.
P(x)
the variable is free to take any value in the domain
24.bound variable - ANSWER ✓ ∀x P(x)
bound to a quantifier.
25.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.
26.summary of De Morgan's laws for quantified statements. - ANSWER ✓ ¬∀x
P(x) ≡ ∃x ¬P(x)
¬∃x P(x) ≡ ∀x ¬P(x)
27.A database is - ANSWER ✓ a large collection of data records that is
searched and manipulated by a computer.
28.The relational database mode - ANSWER ✓ stores data records as relations.
29.The type of data stored in each entry of the n-tuple is called an attribute. -
ANSWER ✓ In the airline example, "flight number" is the first attribute.
30.A key is an attribute or set of attributes that uniquely identifies each n-tuple
in the database. - ANSWER ✓ In the airline example, flight number alone
would not be a key since there are two flights numbered 2262 that leave on
different days.
31.selection operation - ANSWER ✓ select[complete = no]
deletes those set to yes
32.projection operation - ANSWER ✓ project[Date, City]
will delete all Columns but date and city
, 33.unit 7 graphs and trees 20 % - ANSWER ✓
34.undirected graphs - ANSWER ✓ contrasted with the directed graphs of the
previous chapter in the context of relations.
35.Undirected graphs, edges are unordered pairs of vertices, useful for
modeling relationships that are symmetric.
36.note curly braces, remember curly braces means set where order doesn't
matter.
37.{a,b} not directed (a,b) directed edge.
38.graph terminology - ANSWER ✓
39.Adjacent- - ANSWER ✓ if there is an edge between two vertices they are
adjeacent
40.endpoints - ANSWER ✓ Vertices b and e are the endpoints of edge {b, e}.
41.incident - ANSWER ✓ The edge {b, e} is incident to vertices b and e.
42.neighbor - ANSWER ✓ A vertex c is a neighbor of vertex b if {b, c} is an
edge. In the graph above, the neighbors of b are the vertices a, c, and e.
43.degree - ANSWER ✓ number of neighbors a vertex has
44.total degree - ANSWER ✓ the sum of all degrees of the graph
45.regular graph - ANSWER ✓ All vertices have the same degree
46.d-regular graph - ANSWER ✓ all vertices have degree d
47.proposition - ANSWER ✓ A statement that is either true or false.
48.conjunction - ANSWER ✓ The proposition 𝑝∧𝑞 read as "p and q."
STUDY GUIDE 2025/2026 ACCURATE QUESTIONS
AND VERIFIED CORRECT SOLUTIONS WITH
RATIONALES || 100% GUARANTEED PASS
<LATEST VERSION>
1. Commutative Laws - ANSWER ✓ p ∨ q ≡ q ∨ p
p∧q≡q∧p
2. Associative Laws - ANSWER ✓ (p ∨ q) ∨ r ≡ p ∨ (q ∨ r)
(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)
3. Distributive Laws - ANSWER ✓ p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)
p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)
4. Identity Laws - ANSWER ✓ p ∧ 1 ≡ p
p∨0≡p
5. Negation Laws - ANSWER ✓ p ∨ ¬p ≡ 1
p ∧ ¬p ≡ 0
6. Idempotent Laws - ANSWER ✓ p ∨ p ≡ p
p∧p≡p
7. Null Laws - ANSWER ✓ p ∧ 0 ≡ 0
p∨1≡1
8. Absorption Laws - ANSWER ✓ p ∨ (p ∧ q) ≡ p
p ∧ (p ∨ q) ≡ p
9. DeMorgan's Laws - ANSWER ✓ ¬(p ∨ q) ≡ ¬p ∧ ¬q
¬(p ∧ q) ≡ ¬p ∨ ¬q
,10.Involution Law - ANSWER ✓ ¬(¬p) ≡ p
11.Conditional Equivalence - ANSWER ✓ p → q ≡ ¬p ∨ q
12.Contrapositive - ANSWER ✓ p → q ≡ ¬p → ¬q
13.Chain Rule - ANSWER ✓ (p → q) ∧ (q → r) ≡ (p → r)
14.Exclusive or. ⊕ - ANSWER ✓ One or the other, but not both.
We can go to the park or the movies.
15.inclusive or is a: - ANSWER ✓ disjunction
16.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:
17.truth table with three variables - ANSWER ✓ see pic
2^3 rows
18.proposition - ANSWER ✓ p → q
Ex: If it is raining today, the game will be cancelled.
19.Converse: - ANSWER ✓ q → p
If the game is cancelled, it is raining today.
20.Contrapositive - ANSWER ✓ ¬q → ¬p
If the game is not cancelled, then it is not raining today.
21.Inverse: - ANSWER ✓ ¬p → ¬q
If it is not raining today, the game will not be cancelled.
22.biconditional - ANSWER ✓ p ↔ q
, true when P and Q have the same truth value.
see truth table pic.
23.free variable - ANSWER ✓ ex.
P(x)
the variable is free to take any value in the domain
24.bound variable - ANSWER ✓ ∀x P(x)
bound to a quantifier.
25.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.
26.summary of De Morgan's laws for quantified statements. - ANSWER ✓ ¬∀x
P(x) ≡ ∃x ¬P(x)
¬∃x P(x) ≡ ∀x ¬P(x)
27.A database is - ANSWER ✓ a large collection of data records that is
searched and manipulated by a computer.
28.The relational database mode - ANSWER ✓ stores data records as relations.
29.The type of data stored in each entry of the n-tuple is called an attribute. -
ANSWER ✓ In the airline example, "flight number" is the first attribute.
30.A key is an attribute or set of attributes that uniquely identifies each n-tuple
in the database. - ANSWER ✓ In the airline example, flight number alone
would not be a key since there are two flights numbered 2262 that leave on
different days.
31.selection operation - ANSWER ✓ select[complete = no]
deletes those set to yes
32.projection operation - ANSWER ✓ project[Date, City]
will delete all Columns but date and city
, 33.unit 7 graphs and trees 20 % - ANSWER ✓
34.undirected graphs - ANSWER ✓ contrasted with the directed graphs of the
previous chapter in the context of relations.
35.Undirected graphs, edges are unordered pairs of vertices, useful for
modeling relationships that are symmetric.
36.note curly braces, remember curly braces means set where order doesn't
matter.
37.{a,b} not directed (a,b) directed edge.
38.graph terminology - ANSWER ✓
39.Adjacent- - ANSWER ✓ if there is an edge between two vertices they are
adjeacent
40.endpoints - ANSWER ✓ Vertices b and e are the endpoints of edge {b, e}.
41.incident - ANSWER ✓ The edge {b, e} is incident to vertices b and e.
42.neighbor - ANSWER ✓ A vertex c is a neighbor of vertex b if {b, c} is an
edge. In the graph above, the neighbors of b are the vertices a, c, and e.
43.degree - ANSWER ✓ number of neighbors a vertex has
44.total degree - ANSWER ✓ the sum of all degrees of the graph
45.regular graph - ANSWER ✓ All vertices have the same degree
46.d-regular graph - ANSWER ✓ all vertices have degree d
47.proposition - ANSWER ✓ A statement that is either true or false.
48.conjunction - ANSWER ✓ The proposition 𝑝∧𝑞 read as "p and q."
