WGU C277 FINITE MATH1 DISCRETE EXAM 212
QUESTIONS WITH VERIFIED ANSWERS 2026
One or the other, but not both.
We can go to the park or the movies. - CORRECT ANSWER Exclusive or. ⊕
disjunction - CORRECT ANSWER inclusive or is a:
1. ¬ (not)
2. ∧ (and)
3. ∨ (or)
the rule is that negation is applied first, then conjunction, then disjunction: -
CORRECT ANSWER Order of operations in absence of parentheses.
see pic
2^3 rows - CORRECT ANSWER truth table with three variables
p→q
Ex: If it is raining today, the game will be cancelled. - CORRECT ANSWER
proposition
q→p
If the game is cancelled, it is raining today. - CORRECT ANSWER Converse:
,¬q → ¬p
If the game is not cancelled, then it is not raining today. - CORRECT ANSWER
Contrapositive
¬p → ¬q
If it is not raining today, the game will not be cancelled. - CORRECT ANSWER
Inverse:
p↔q
true when P and Q have the same truth value.
see truth table pic. - CORRECT ANSWER biconditional
ex.
P(x)
the variable is free to take any value in the domain - CORRECT ANSWER free
variable
∀x P(x)
bound to a quantifier. - CORRECT ANSWER bound variable
,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. - CORRECT ANSWER
In the statement (∀x P(x)) ∧ Q(x),
¬∀x P(x) ≡ ∃x ¬P(x)
¬∃x P(x) ≡ ∀x ¬P(x) - CORRECT ANSWER summary of De Morgan's laws for
quantified statements.
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.
, hypotheses don’t always all need to be true, see example. but every time all the
hypotheses are true, the conclusion needs to be true as well. - CORRECT ANSWER
using a truth table to establish the validity of an argument
see pic. - CORRECT ANSWER rules of inference.
any statement that you can prove - CORRECT ANSWER theorem
A proof consists of a series of steps, each of which follows logically from
assumptions, or from previously proven statements, whose final step should
result in the statement of the theorem being proven. - CORRECT ANSWER proof
which are statements assumed to be true. - CORRECT ANSWER the proof of a
theorem may make use of axioms:
trying everything in the given universe. - CORRECT ANSWER proofs by exhaustion
show that one fails.
A counterexample is an assignment of values to variables that shows that a
universal statement is false.
A counterexample for a conditional statement must satisfy all the hypotheses and
contradict the conclusion. - CORRECT ANSWER proofs by counter example
used for conditional statements
QUESTIONS WITH VERIFIED ANSWERS 2026
One or the other, but not both.
We can go to the park or the movies. - CORRECT ANSWER Exclusive or. ⊕
disjunction - CORRECT ANSWER inclusive or is a:
1. ¬ (not)
2. ∧ (and)
3. ∨ (or)
the rule is that negation is applied first, then conjunction, then disjunction: -
CORRECT ANSWER Order of operations in absence of parentheses.
see pic
2^3 rows - CORRECT ANSWER truth table with three variables
p→q
Ex: If it is raining today, the game will be cancelled. - CORRECT ANSWER
proposition
q→p
If the game is cancelled, it is raining today. - CORRECT ANSWER Converse:
,¬q → ¬p
If the game is not cancelled, then it is not raining today. - CORRECT ANSWER
Contrapositive
¬p → ¬q
If it is not raining today, the game will not be cancelled. - CORRECT ANSWER
Inverse:
p↔q
true when P and Q have the same truth value.
see truth table pic. - CORRECT ANSWER biconditional
ex.
P(x)
the variable is free to take any value in the domain - CORRECT ANSWER free
variable
∀x P(x)
bound to a quantifier. - CORRECT ANSWER bound variable
,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. - CORRECT ANSWER
In the statement (∀x P(x)) ∧ Q(x),
¬∀x P(x) ≡ ∃x ¬P(x)
¬∃x P(x) ≡ ∀x ¬P(x) - CORRECT ANSWER summary of De Morgan's laws for
quantified statements.
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.
, hypotheses don’t always all need to be true, see example. but every time all the
hypotheses are true, the conclusion needs to be true as well. - CORRECT ANSWER
using a truth table to establish the validity of an argument
see pic. - CORRECT ANSWER rules of inference.
any statement that you can prove - CORRECT ANSWER theorem
A proof consists of a series of steps, each of which follows logically from
assumptions, or from previously proven statements, whose final step should
result in the statement of the theorem being proven. - CORRECT ANSWER proof
which are statements assumed to be true. - CORRECT ANSWER the proof of a
theorem may make use of axioms:
trying everything in the given universe. - CORRECT ANSWER proofs by exhaustion
show that one fails.
A counterexample is an assignment of values to variables that shows that a
universal statement is false.
A counterexample for a conditional statement must satisfy all the hypotheses and
contradict the conclusion. - CORRECT ANSWER proofs by counter example
used for conditional statements
