WGU D420:Discrete Math 1, Terms defined and Clearly Explained!!LATEST 2024 VERSION
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WGU D420
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WGU D420
WGU D420:Discrete Math 1, Terms defined and Clearly Explained!!LATEST 2024 VERSION
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)
...
WGU D420:Discrete Math 1, All Terms
defined and Clearly Explained!!
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
A
VI
Order of operations in absence of parentheses. - ANS 1. ¬ (not)
2. ∧ (and)
3. ∨ (or)
TU
the rule is that negation is applied first, then conjunction, then disjunction:
truth table with three variables - ANS see pic
IS
2^3 rows
OM
proposition - ANS p → q
Ex: If it is raining today, the game will be cancelled.
Converse: - ANS q → p
NA
If the game is cancelled, it is raining today.
JP
Contrapositive - 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 - ANS ex.
P(x)
A
the variable is free to take any value in the domain
VI
bound variable - ANS ∀x P(x)
bound to a quantifier.
TU
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.
IS
this statement is not a proposition cause of the free variable.
OM
summary of De Morgan's laws for quantified statements. - ANS ¬∀x P(x) ≡ ∃x ¬P(x)
¬∃x P(x) ≡ ∀x ¬P(x)
using a truth table to establish the validity of an argument - ANS see pic.
NA
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.
JP
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. - ANS see pic.
A
VI
theorem - ANS any statement that you can prove
proof - ANS A proof consists of a series of steps, each of which follows logically from
TU
assumptions, or from previously proven statements, whose final step should result in
the statement of the theorem being proven.
IS
the proof of a theorem may make use of axioms: - ANS which are statements
assumed to be true.
OM
proofs by exhaustion - ANS trying everything in the given universe.
proofs by counter example - ANS show that one fails.
NA
A counterexample is an assignment of values to variables that shows that a universal
statement is false.
JP
A counterexample for a conditional statement must satisfy all the hypotheses and
contradict the conclusion.
direct proofs - ANS used for conditional statements
If p then q
Assume p
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