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WGU Discrete Math 1 Exam 212 Questions with Verified Answers,100% CORRECT
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WGU Discrete Math 1 Exam 212 Questions with Verified Answers
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WGU Discrete Math 1 Exam 212 Questions with VerifiedAnswers
Exclusive or. ⊕ - CORRECT ANSWER One or the other, but not both.
We can go to the park or the movies.
inclusive or is a: - CORRECT ANSWER disjunction
Order of operations in absence of parentheses. - CORRECT ANSWER 1. ¬ (not)
2. ∧ (and)
3. ∨ (or)
the rule is that negation is applied first, then conjunction, then disjunction:
truth table with three variables - CORRECT ANSWER see pic
2^3 rows
proposition - CORRECT ANSWER p → q
Ex: If it is raining today, the game will be cancelled.
Converse: - CORRECT ANSWER q → p
If the game is cancelled, it is raining today.
Contrapositive - CORRECT ANSWER ¬q → ¬p
If the game is not cancelled, then it is not raining today.
Inverse: - CORRECT ANSWER ¬p → ¬q
If it is not raining today, the game will not be cancelled.
biconditional - CORRECT ANSWER p ↔ q
true when P and Q have the same truth value.
,see truth table pic.
free variable - CORRECT ANSWER ex.
P(x)
the variable is free to take any value in the domain
bound variable - CORRECT ANSWER ∀x P(x)
bound to a quantifier.
In the statement (∀x P(x)) ∧ Q(x), - CORRECT 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. - CORRECT ANSWER ¬∀x
P(x) ≡ ∃x ¬P(x)
¬∃x P(x) ≡ ∀x ¬P(x)
using a truth table to establish the validity of an argument - CORRECT 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. - CORRECT ANSWER see pic.
theorem - CORRECT ANSWER any statement that you can prove
proof - CORRECT ANSWER 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.
the proof of a theorem may make use of axioms: - CORRECT ANSWER which are
statements assumed to be true.
proofs by exhaustion - CORRECT ANSWER trying everything in the given universe.
proofs by counter example - CORRECT ANSWER 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.
direct proofs - CORRECT ANSWER used for conditional statements
If p then q
Assume p
Therefore q
proofs by contrapositive - CORRECT ANSWER proves a conditional theorem of the
form p → q by showing that the contrapositive ¬q → ¬p is true. In other words, ¬c
is assumed to be true and ¬p is proven as a result of ¬q.
Logically equivalent to if p then q
proof by contradiction - CORRECT ANSWER (indirect proof)
starts by assuming that the theorem is false and then shows that some logical
inconsistency arises as a result of this assumption.
Notice not a conditional.
Want to prove Y
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