WGU D420 Discrete Math: Logic
Questions and Answers 100% Pass
What is a tautology in logic?
✔✔A tautology is a statement that is always true, regardless of the truth values of its
components.
What is the contrapositive of a conditional statement?
✔✔The contrapositive of a conditional statement is formed by negating both the hypothesis and
conclusion, and then reversing them.
How does a conjunction work in logic?
✔✔A conjunction is true only if both component statements are true.
What is a biconditional statement?
✔✔A biconditional statement is true when both parts (the hypothesis and conclusion) have the
same truth value.
What is the difference between the converse and the inverse of a conditional statement?
1
,✔✔The converse swaps the hypothesis and conclusion, while the inverse negates both without
swapping.
What does De Morgan's Law state?
✔✔De Morgan's Law states that the negation of a conjunction is equivalent to the disjunction of
the negations, and vice versa.
What does a truth table represent?
✔✔A truth table represents all possible truth values of a logical expression based on the truth
values of its components.
How does a disjunction work in logic?
✔✔A disjunction is true if at least one of its component statements is true.
What is the universal quantifier in predicate logic?
✔✔The universal quantifier expresses that a statement applies to all elements within a particular
set.
What does the existential quantifier indicate in logic?
2
, ✔✔The existential quantifier asserts that there exists at least one element in a set for which a
statement is true.
What is logical equivalence?
✔✔Logical equivalence means that two statements always have the same truth value in every
possible situation.
What is the purpose of a proof in discrete mathematics?
✔✔A proof is used to demonstrate the validity or truth of a mathematical statement using logical
reasoning.
What does modus ponens allow you to conclude?
✔✔Modus ponens allows you to conclude the consequent if the antecedent is true in a
conditional statement.
What is an implication in logic?
✔✔An implication is a logical statement of the form "If P, then Q," where Q follows from P.
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Questions and Answers 100% Pass
What is a tautology in logic?
✔✔A tautology is a statement that is always true, regardless of the truth values of its
components.
What is the contrapositive of a conditional statement?
✔✔The contrapositive of a conditional statement is formed by negating both the hypothesis and
conclusion, and then reversing them.
How does a conjunction work in logic?
✔✔A conjunction is true only if both component statements are true.
What is a biconditional statement?
✔✔A biconditional statement is true when both parts (the hypothesis and conclusion) have the
same truth value.
What is the difference between the converse and the inverse of a conditional statement?
1
,✔✔The converse swaps the hypothesis and conclusion, while the inverse negates both without
swapping.
What does De Morgan's Law state?
✔✔De Morgan's Law states that the negation of a conjunction is equivalent to the disjunction of
the negations, and vice versa.
What does a truth table represent?
✔✔A truth table represents all possible truth values of a logical expression based on the truth
values of its components.
How does a disjunction work in logic?
✔✔A disjunction is true if at least one of its component statements is true.
What is the universal quantifier in predicate logic?
✔✔The universal quantifier expresses that a statement applies to all elements within a particular
set.
What does the existential quantifier indicate in logic?
2
, ✔✔The existential quantifier asserts that there exists at least one element in a set for which a
statement is true.
What is logical equivalence?
✔✔Logical equivalence means that two statements always have the same truth value in every
possible situation.
What is the purpose of a proof in discrete mathematics?
✔✔A proof is used to demonstrate the validity or truth of a mathematical statement using logical
reasoning.
What does modus ponens allow you to conclude?
✔✔Modus ponens allows you to conclude the consequent if the antecedent is true in a
conditional statement.
What is an implication in logic?
✔✔An implication is a logical statement of the form "If P, then Q," where Q follows from P.
3
