Exam (elaborations)
WGU Discrete Math 1 Exam 212 Questions with Verified Answers,100% CORRECT
- Course
- Institution
WGU Discrete Math 1 Exam 212 Questions with Verified Answers
[Show more]
Content preview
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
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller paulhans. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $16.49. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
80364 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now