WGU D420 DISCRETE LATEST
MATH 1
Exclusive or. ⊕ - ANSWERS-One or the other, but not both.
We can go to the park or the movies.
inclusive or is a: - ANSWERS-disjunction
Order of operations in absence of parentheses. - ANSWERS-1. ¬ (not)
2. ∧ (and)
3. ∨ (or)
the rule is that negation is applied first, then conjunction, then
disjunction:
truth table with three variables - ANSWERS-see pic
2^3 rows
proposition - ANSWERS-p → q
Ex: If it is raining today, the game will be cancelled.
Converse: - ANSWERS-q → p
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1
, WGU D420 DISCRETE LATEST
MATH 1
If the game is cancelled, it is raining today.
Contrapositive - ANSWERS-¬q → ¬p
If the game is not cancelled, then it is not raining today.
Inverse: - ANSWERS-¬p → ¬q
If it is not raining today, the game will not be cancelled.
biconditional - ANSWERS-p ↔ q
true when P and Q have the same truth value.
see truth table pic.
free variable - ANSWERS-ex.
P(x)
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2
, WGU D420 DISCRETE LATEST
MATH 1
the variable is free to take any value in the domain
bound variable - ANSWERS-∀x P(x)
bound to a quantifier.
In the statement (∀x P(x)) ∧ Q(x), - ANSWERS-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. - ANSWERS-
¬∀x P(x) ≡ ∃x ¬P(x)
¬∃x P(x) ≡ ∀x ¬P(x)
using a truth table to establish the validity of an argument - ANSWERS-
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.
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3
, WGU D420 DISCRETE LATEST
MATH 1
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. - ANSWERS-see pic.
theorem - ANSWERS-any statement that you can prove
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PAGE
4
MATH 1
Exclusive or. ⊕ - ANSWERS-One or the other, but not both.
We can go to the park or the movies.
inclusive or is a: - ANSWERS-disjunction
Order of operations in absence of parentheses. - ANSWERS-1. ¬ (not)
2. ∧ (and)
3. ∨ (or)
the rule is that negation is applied first, then conjunction, then
disjunction:
truth table with three variables - ANSWERS-see pic
2^3 rows
proposition - ANSWERS-p → q
Ex: If it is raining today, the game will be cancelled.
Converse: - ANSWERS-q → p
END OF
PAGE
1
, WGU D420 DISCRETE LATEST
MATH 1
If the game is cancelled, it is raining today.
Contrapositive - ANSWERS-¬q → ¬p
If the game is not cancelled, then it is not raining today.
Inverse: - ANSWERS-¬p → ¬q
If it is not raining today, the game will not be cancelled.
biconditional - ANSWERS-p ↔ q
true when P and Q have the same truth value.
see truth table pic.
free variable - ANSWERS-ex.
P(x)
END OF
PAGE
2
, WGU D420 DISCRETE LATEST
MATH 1
the variable is free to take any value in the domain
bound variable - ANSWERS-∀x P(x)
bound to a quantifier.
In the statement (∀x P(x)) ∧ Q(x), - ANSWERS-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. - ANSWERS-
¬∀x P(x) ≡ ∃x ¬P(x)
¬∃x P(x) ≡ ∀x ¬P(x)
using a truth table to establish the validity of an argument - ANSWERS-
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.
END OF
PAGE
3
, WGU D420 DISCRETE LATEST
MATH 1
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. - ANSWERS-see pic.
theorem - ANSWERS-any statement that you can prove
END OF
PAGE
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