INDUMAT (Quiz 1) Flashcards
Z
Set of integers (…..,-3,-2,-1,0,1,2,3,…….)
N
Set of nonnegative integers or natural numbers (1,2,3,4,….)
Z^+
Set of positive integers (1,2,3) ; not including 0
R
Set of real numbers (numbers with decimal expansion)
R^+
Set of positive real numbers
R^*
Set of nonzero real numbers
Q
Set of rational numbers (numbers including fractions)
Law of Double Negation (Set Theory)
(A’)’ = A
De Morgan’s Laws (Set Theory)
(A U B)’ = A’ ∩ B’
(A ∩ B)’ = A’ U B’
Commutative Laws (Set Theory)
A U B = B U A
A ∩ B = B ∩ A
Associative Laws (Set Theory)
A U (B U C) = (A U B) U C
A ∩ (B ∩ C) = (A ∩ B) ∩ C
Distributive Laws (Set Theory)
A ∩ (B U C) = (A ∩ B) U (A ∩ C)
A U (B ∩ C) = (A U B) ∩ (A U C)
Idempotent Laws (Set Theory)
A U A = A
A ∩ A = A
Identity Laws (Set Theory)
A U Null set = A
A ∩ Universe = A
Inverse Laws (Set Theory)
A U A’ = Universe
A ∩ A’ = Null Set
Domination Laws (Set Theory)
A U Universe = Universe
A ∩ Null Set = Null Set
Absorption Laws (Set Theory)
A U (A ∩ B) = A
A Int (A U B) = A
U
Union (or)
∩
Intersection (and)
∈
is an element of/belongs to
⊂
Proper subset
And
ʌ
⊆
Subset
Or
v
Implies
=>
{ }
Empty set/Null set
△
Symmetric Difference
A △ B = (A-B) U (B-A) or (A U B) - (A ∩ B)
If and Only if
<=>
Law of Double Negation (Laws of Logic)
¬¬ p 三 p
It is not the case that / not
¬
Or - form of an implication (Laws of Logic)
p → q 三 ¬ p v q
Contrapositive form of an implication (Laws of Logic)
p → q 三 ¬ p → ¬ q
De Morgan’s Law (Laws of Logic)
¬ (p v q) 三 ¬ p ʌ ¬ q
¬ (p ʌ q) 三 ¬ p v ¬ q
Rule for Direct Proof (Laws of Logic)
(p ʌ r) → q 三 r → (p → q)
Rule for Proof by Contradiction (Laws of Logic)
(p ʌ ¬ q → o) 三 (p → q)
Commutative Laws (Laws of Logic)
p v q 三 q v p
p ʌ q 三 q ʌ p
Associative Laws (Laws of Logic)
p v (q v r) 三 (p v q) v r
p ʌ (q ʌ r) 三 (p ʌ q) ʌ r
Distributive Laws (Laws of Logic)
p v (q ʌ r) 三 (p v q) ʌ (p v r)
p ʌ (q v r) 三 (p ʌ q) v (p ʌ r)
Idempotent Laws (Laws of Logic)
p v p 三 p
p ʌ p 三 p
Identity Laws (Laws of Logic)
p v o 三 p
p ʌ I 三 p
Inverse Laws (Laws of Logic)
p v ¬ p 三 I
p ʌ ¬ p 三 o
Domination Laws (Laws of Logic)
p v I 三 I
p ʌ o 三 o
Absorption Laws (Laws of Logic)
p v (p ʌ q) 三 p
p ʌ (p v q) 三 p
“o” (Laws of Logic)
Statement that is always false
In a truth table, what is the mathematical approach in evaluating conjunction (p ʌ q)?
min (p,q)
In a truth table, what is the mathematical approach in evaluating disjunction (p v q)?
max (p,q)
In a truth table, what is the mathematical approach in evaluating conditional (p → q)?
True if and only if the val (p) is less than or equal to val (q)
In a truth table, how do you evaluate a biconditional (p <=> q)?
True if both statements have the same truth value. (Both p and q are true or both q and p are false). Otherwise, it is false.
Although
ʌ
But
ʌ
Even though
ʌ
However
ʌ
Unless
v
When ………, then…….
→
Provided that ………. , then ………
→
Just in case that
<=>
“I” (Laws of Logic)
A statement that is always true
In a truth table, if all the outputs of a column are true, then it is a _________
Tautology
In a truth table, if all the outputs of a column are false, then it is a _________
Contradiction
In a truth table, if the outputs have at least one true and one false, then it is a _________
Contingent
Converse and Inverse are examples of _________.
Invalid Arguments
Given p → q, this is an example of a _________.
Conditional
Given p → q, the inverse would be _________
¬ p → ¬ q (Negation)
Given p → q, the converse would be _________
q → p (Swap)
Given p → q, the contrapositive would be _________
¬ q → ¬ p (Negation and Swap)
[p ʌ (p → q)] → q (Rule of Inference)
Modus Ponens
[(p → q) ʌ (q → r)] → (p → r) (Rule of Inference)
Law of Syllogism
[(p → q) ʌ ¬ q] → ¬ p (Rule of Inference)
Modus Tollens
[¬ p → 0] → p (Rule of Inference)
Rule of Contradiction
(p ʌ q) → p (Rule of Inference)
Rule of Conjunctive Simplification
[(p v q) ʌ ¬ p] → q (Rule of Inference)
Rule of Disjunctive Syllogism
[(p ʌ q) ʌ [p → (q → r)]] → r (Rule of Inference)
Rule of Conditional proof
[(p → r) ʌ (q → r)] → [(p v q) → r] (Rule of Inference)
Rule for Proof by Cases
p → p v q (Rule of Inference)
Rule of Disjunctive Amplification
[(p → q) ʌ (r → s) ʌ (p v r)] → (q v s) (Rule of Inference)
Rule of Constructive Dilemma
[(p → q) ʌ (r → s) ʌ (¬ q v ¬ s)] → (¬ p v ¬ r) (Rule of Inference)
Rule of Destructive Dilemma
A - B is the same as
A Int B’
