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WGU D420 DISCRETE MA TH 1
EXAM QUESTIONS AND A NSWERS
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Question :Exclusive or. ⊕
Correct answer:One or the other, but not both.
We can go to the park or the movies.
Question :inclusive or is a:
Correct answer:disjunction
Question :Order of operations in absence of parentheses.
Correct answer:1. ¬ (not)
- ∧ (and)
- ∨ (or)
the rule is that negation is applied first, then conjunction,
then disjunction:
Question :truth table with three variables
Correct answer:see pic
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2^3 rows
Question :proposition
Correct answer:p → q
Ex: If it is raining today, the game will be cancelled.
Question :Converse:
Correct answer:q → p
If the game is cancelled, it is raining today.
Question :Contrapositive
Correct answer:¬q → ¬p
If the game is not cancelled, then it is not raining today.
Question :Inverse:
Correct answer:¬p → ¬q
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If it is not raining today, the game will not be cancelled.
Question :biconditional
Correct answer:p ↔ q
true when P and Q have the same truth value.
see truth table pic.
Question :free variable
Correct answer:ex.
P(x) the variable is free to take any value in the domain
Question :bound variable
Correct answer:∀x P(x)
bound to a quantifier.
Question :In the statement (∀x P(x)) ∧ Q(x),
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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.
Question :summary of De Morgan's laws for quantified
statements.
Correct answer:¬∀x P(x) ≡ ∃x ¬P(x)
¬∃x P(x) ≡ ∀x ¬P(x)
Question :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.