WGU D420 DISCRETE MATH LOGIC | 2025-2026 LATEST UPDATED| ACTUAL EXAM
COMPLETE QUESTIONS AND ANSWERS | 100% RATED CORRECT | 100% VERFIED |
ALREADY GRADED A+|GET A
1. proposition: a statement that is either true or false
2. ^: and
3. v: or
4. ¬: negation
5. ’: conditional operation, "if p, then q"
6. Equivalent English expressions that mean "if p, then q": If p, q q, if p p
implies q p only if q p is sufficient for q q is necessary for p
7. in a conditional proposition "’" p is the _______ and q is the __________:
is the hypothesis and q is the conclusion
8. The converse is the opposite of the conditional statement: For example,
the converse of p ’ q (if p then q) is q ’ p (if q then p). If p ’ q is true, it does NOT
guarantee that q ’ p is true
, 9. The inverse is the negation of the conditional statement: For example, the
inverse of p ’ q (if p then q) is ¬p ’ ¬q (if not p then not q). If p ’ q is true, it does
NOT guarantee that ¬p ’ ¬q is true
10. The contrapositive is the opposite and negative of the conditional
statement: For example, the contrapositive of p ’ q (if p then q) is ¬q ’ ¬p (if no
q then not p). If p ’ q is true, it DOES guarantee that ¬q ’ ¬p is true
11. biconditional operation: is read "p is necessary and sufficient for q" or "if p
then q, and conversely" or "p if and only if q"
12. Logical equivalence p qa : Two compound propositions are logically
equivalent if they have the same truth value. That is, the truth value in the final
column in a truth table is the same for both compound propositions
13. tautology: If the compound propositions is always true. For example, p(¬p.
14. contradiction: if the compound proposition is always false. For example, p'¬p.
15. De Morgan's Law: logical equivalences that show how to correctly distribute a
negation operation inside a parenthesized expression containing the disjunction
or conjunction operator. ¬(p ( q) = (¬p ' ¬q)
¬(p ' q) = (¬p ( ¬q)
16. Absorption laws: p ( (p ' q) a p
p ' (p ( q) a p
17. Associative laws: (p ( q) ( r a p ( (q ( r)
(p ' q) ' r a p ' (q ' r)
18. Commutative laws: p ( q a q ( p
p'qaq'p
19. Complement laws: p ' ¬p a F
¬T a F
p ( ¬p a T
¬F a T
20. Conditional identities: p ’ q a ¬p ( q
COMPLETE QUESTIONS AND ANSWERS | 100% RATED CORRECT | 100% VERFIED |
ALREADY GRADED A+|GET A
1. proposition: a statement that is either true or false
2. ^: and
3. v: or
4. ¬: negation
5. ’: conditional operation, "if p, then q"
6. Equivalent English expressions that mean "if p, then q": If p, q q, if p p
implies q p only if q p is sufficient for q q is necessary for p
7. in a conditional proposition "’" p is the _______ and q is the __________:
is the hypothesis and q is the conclusion
8. The converse is the opposite of the conditional statement: For example,
the converse of p ’ q (if p then q) is q ’ p (if q then p). If p ’ q is true, it does NOT
guarantee that q ’ p is true
, 9. The inverse is the negation of the conditional statement: For example, the
inverse of p ’ q (if p then q) is ¬p ’ ¬q (if not p then not q). If p ’ q is true, it does
NOT guarantee that ¬p ’ ¬q is true
10. The contrapositive is the opposite and negative of the conditional
statement: For example, the contrapositive of p ’ q (if p then q) is ¬q ’ ¬p (if no
q then not p). If p ’ q is true, it DOES guarantee that ¬q ’ ¬p is true
11. biconditional operation: is read "p is necessary and sufficient for q" or "if p
then q, and conversely" or "p if and only if q"
12. Logical equivalence p qa : Two compound propositions are logically
equivalent if they have the same truth value. That is, the truth value in the final
column in a truth table is the same for both compound propositions
13. tautology: If the compound propositions is always true. For example, p(¬p.
14. contradiction: if the compound proposition is always false. For example, p'¬p.
15. De Morgan's Law: logical equivalences that show how to correctly distribute a
negation operation inside a parenthesized expression containing the disjunction
or conjunction operator. ¬(p ( q) = (¬p ' ¬q)
¬(p ' q) = (¬p ( ¬q)
16. Absorption laws: p ( (p ' q) a p
p ' (p ( q) a p
17. Associative laws: (p ( q) ( r a p ( (q ( r)
(p ' q) ' r a p ' (q ' r)
18. Commutative laws: p ( q a q ( p
p'qaq'p
19. Complement laws: p ' ¬p a F
¬T a F
p ( ¬p a T
¬F a T
20. Conditional identities: p ’ q a ¬p ( q
