D420 discrete math 1 wgu Questions and Correct Answers/ Latest Update / Already Graded

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D420 discrete math 1 wgu Questions
and Correct Answers/ Latest Update /
Already Graded
Exclusive or. ⊕


Ans: One or the other, but not both.


We can go to the park or the movies.




inclusive or is a:


Ans: disjunction




Order of operations in absence of parentheses.


Ans: 1. ¬ (not)


2. ∧ (and)


3. ∨ (or)


the rule is that negation is applied first, then conjunction, then disjunction:

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truth table with three variables


Ans: see pic


2^3 rows




proposition


Ans: p → q


Ex: If it is raining today, the game will be cancelled.




Converse:


Ans: q → p




If the game is cancelled, it is raining today.




Contrapositive

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Ans: ¬q → ¬p




If the game is not cancelled, then it is not raining today.




Inverse:


Ans: ¬p → ¬q




If it is not raining today, the game will not be cancelled.




biconditional


Ans: p ↔ q


true when P and Q have the same truth value.




see truth table pic.




free variable

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Ans: ex.


P(x)


the variable is free to take any value in the domain




bound variable


Ans: ∀x P(x)


bound to a quantifier.




In the statement (∀x P(x)) ∧ Q(x),


Ans: 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.