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Term 1 (2023-2024) > INDUMAT (Quiz 1) > Flashcards

INDUMAT (Quiz 1) Flashcards

1
Q

Z

A

Set of integers (…..,-3,-2,-1,0,1,2,3,…….)

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2
Q

N

A

Set of nonnegative integers or natural numbers (1,2,3,4,….)

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3
Q

Z^+

A

Set of positive integers (1,2,3) ; not including 0

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4
Q

R

A

Set of real numbers (numbers with decimal expansion)

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5
Q

R^+

A

Set of positive real numbers

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6
Q

R^*

A

Set of nonzero real numbers

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7
Q

Q

A

Set of rational numbers (numbers including fractions)

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8
Q

Law of Double Negation (Set Theory)

A

(A’)’ = A

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9
Q

De Morgan’s Laws (Set Theory)

A

(A U B)’ = A’ ∩ B’
(A ∩ B)’ = A’ U B’

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10
Q

Commutative Laws (Set Theory)

A

A U B = B U A
A ∩ B = B ∩ A

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11
Q

Associative Laws (Set Theory)

A

A U (B U C) = (A U B) U C
A ∩ (B ∩ C) = (A ∩ B) ∩ C

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12
Q

Distributive Laws (Set Theory)

A

A ∩ (B U C) = (A ∩ B) U (A ∩ C)
A U (B ∩ C) = (A U B) ∩ (A U C)

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13
Q

Idempotent Laws (Set Theory)

A

A U A = A
A ∩ A = A

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14
Q

Identity Laws (Set Theory)

A

A U Null set = A
A ∩ Universe = A

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15
Q

Inverse Laws (Set Theory)

A

A U A’ = Universe
A ∩ A’ = Null Set

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16
Q

Domination Laws (Set Theory)

A

A U Universe = Universe
A ∩ Null Set = Null Set

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17
Q

Absorption Laws (Set Theory)

A

A U (A ∩ B) = A
A Int (A U B) = A

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18
Q

U

A

Union (or)

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19
Q

∩

A

Intersection (and)

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20
Q

∈

A

is an element of/belongs to

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21
Q

⊂

A

Proper subset

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22
Q

And

A

ʌ

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23
Q

⊆

A

Subset

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24
Q

Or

A

v

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25
Q

Implies

A

=>

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26
Q

{ }

A

Empty set/Null set

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27
Q

△

A

Symmetric Difference
A △ B = (A-B) U (B-A) or (A U B) - (A ∩ B)

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28
Q

If and Only if

A

<=>

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29
Q

Law of Double Negation (Laws of Logic)

A

¬¬ p 三 p

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30
Q

It is not the case that / not

A

¬

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31
Q

Or - form of an implication (Laws of Logic)

A

p → q 三 ¬ p v q

32
Q

Contrapositive form of an implication (Laws of Logic)

A

p → q 三 ¬ p → ¬ q

33
Q

De Morgan’s Law (Laws of Logic)

A

¬ (p v q) 三 ¬ p ʌ ¬ q
¬ (p ʌ q) 三 ¬ p v ¬ q

34
Q

Rule for Direct Proof (Laws of Logic)

A

(p ʌ r) → q 三 r → (p → q)

35
Q

Rule for Proof by Contradiction (Laws of Logic)

A

(p ʌ ¬ q → o) 三 (p → q)

36
Q

Commutative Laws (Laws of Logic)

A

p v q 三 q v p
p ʌ q 三 q ʌ p

37
Q

Associative Laws (Laws of Logic)

A

p v (q v r) 三 (p v q) v r
p ʌ (q ʌ r) 三 (p ʌ q) ʌ r

38
Q

Distributive Laws (Laws of Logic)

A

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)

39
Q

Idempotent Laws (Laws of Logic)

A

p v p 三 p
p ʌ p 三 p

40
Q

Identity Laws (Laws of Logic)

A

p v o 三 p
p ʌ I 三 p

41
Q

Inverse Laws (Laws of Logic)

A

p v ¬ p 三 I
p ʌ ¬ p 三 o

42
Q

Domination Laws (Laws of Logic)

A

p v I 三 I
p ʌ o 三 o

43
Q

Absorption Laws (Laws of Logic)

A

p v (p ʌ q) 三 p
p ʌ (p v q) 三 p

44
Q

“o” (Laws of Logic)

A

Statement that is always false

45
Q

In a truth table, what is the mathematical approach in evaluating conjunction (p ʌ q)?

A

min (p,q)

46
Q

In a truth table, what is the mathematical approach in evaluating disjunction (p v q)?

A

max (p,q)

47
Q

In a truth table, what is the mathematical approach in evaluating conditional (p → q)?

A

True if and only if the val (p) is less than or equal to val (q)

48
Q

In a truth table, how do you evaluate a biconditional (p <=> q)?

A

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.

49
Q

Although

A

ʌ

50
Q

But

A

ʌ

51
Q

Even though

A

ʌ

52
Q

However

A

ʌ

53
Q

Unless

A

v

54
Q

When ………, then…….

A

→

55
Q

Provided that ………. , then ………

A

→

56
Q

Just in case that

A

<=>

57
Q

“I” (Laws of Logic)

A

A statement that is always true

58
Q

In a truth table, if all the outputs of a column are true, then it is a _________

A

Tautology

59
Q

In a truth table, if all the outputs of a column are false, then it is a _________

A

Contradiction

60
Q

In a truth table, if the outputs have at least one true and one false, then it is a _________

A

Contingent

61
Q

Converse and Inverse are examples of _________.

A

Invalid Arguments

62
Q

Given p → q, this is an example of a _________.

A

Conditional

63
Q

Given p → q, the inverse would be _________

A

¬ p → ¬ q (Negation)

64
Q

Given p → q, the converse would be _________

A

q → p (Swap)

65
Q

Given p → q, the contrapositive would be _________

A

¬ q → ¬ p (Negation and Swap)

66
Q

[p ʌ (p → q)] → q (Rule of Inference)

A

Modus Ponens

67
Q

[(p → q) ʌ (q → r)] → (p → r) (Rule of Inference)

A

Law of Syllogism

68
Q

[(p → q) ʌ ¬ q] → ¬ p (Rule of Inference)

A

Modus Tollens

69
Q

[¬ p → 0] → p (Rule of Inference)

A

Rule of Contradiction

69
Q

(p ʌ q) → p (Rule of Inference)

A

Rule of Conjunctive Simplification

69
Q

[(p v q) ʌ ¬ p] → q (Rule of Inference)

A

Rule of Disjunctive Syllogism

69
Q

[(p ʌ q) ʌ [p → (q → r)]] → r (Rule of Inference)

A

Rule of Conditional proof

69
Q

[(p → r) ʌ (q → r)] → [(p v q) → r] (Rule of Inference)

A

Rule for Proof by Cases

69
Q

p → p v q (Rule of Inference)

A

Rule of Disjunctive Amplification

69
Q

[(p → q) ʌ (r → s) ʌ (p v r)] → (q v s) (Rule of Inference)

A

Rule of Constructive Dilemma

69
Q

[(p → q) ʌ (r → s) ʌ (¬ q v ¬ s)] → (¬ p v ¬ r) (Rule of Inference)

A

Rule of Destructive Dilemma

70
Q

A - B is the same as

A

A Int B’

Term 1 (2023-2024) (18 decks)

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