WGU C960 DISCRETE MATHEMATICS II
EXAM SCRIPT WITH VERIFIED QUESTIONS
AND ANSWERS
●● inclusive or is a:
Answer: disjunction
●● 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:
●● 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
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
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.
, 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 dont always all need to be true, see example. but every time
all the hypotheses are true, the conclusion needs to be true as well.
●● rules of inference.
Answer: see pic.
●● theorem
Answer: any statement that you can prove
●● proof
Answer: A proof consists of a series of steps, each of which follows
logically from assumptions, or from previously proven statements,
EXAM SCRIPT WITH VERIFIED QUESTIONS
AND ANSWERS
●● inclusive or is a:
Answer: disjunction
●● 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:
●● 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
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
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.
, 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 dont always all need to be true, see example. but every time
all the hypotheses are true, the conclusion needs to be true as well.
●● rules of inference.
Answer: see pic.
●● theorem
Answer: any statement that you can prove
●● proof
Answer: A proof consists of a series of steps, each of which follows
logically from assumptions, or from previously proven statements,
