INDUMAT (Quiz 1)

Question 1

Z

Answer 1

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

Question 2

N

Answer 2

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

Question 3

Z^+

Answer 3

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

Question 4

R

Answer 4

Set of real numbers (numbers with decimal expansion)

Question 5

R^+

Answer 5

Set of positive real numbers

Question 6

R^*

Answer 6

Set of nonzero real numbers

Question 7

Q

Answer 7

Set of rational numbers (numbers including fractions)

Question 8

Law of Double Negation (Set Theory)

Answer 8

(A’)’ = A

Question 9

De Morgan’s Laws (Set Theory)

Answer 9

(A U B)’ = A’ ∩ B’
(A ∩ B)’ = A’ U B’

Question 10

Commutative Laws (Set Theory)

Answer 10

A U B = B U A
A ∩ B = B ∩ A

Question 11

Associative Laws (Set Theory)

Answer 11

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

Question 12

Distributive Laws (Set Theory)

Answer 12

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

Question 13

Idempotent Laws (Set Theory)

Answer 13

A U A = A
A ∩ A = A

Question 14

Identity Laws (Set Theory)

Answer 14

A U Null set = A
A ∩ Universe = A

Question 15

Inverse Laws (Set Theory)

Answer 15

A U A’ = Universe
A ∩ A’ = Null Set

Question 16

Domination Laws (Set Theory)

Answer 16

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

Question 17

Absorption Laws (Set Theory)

Answer 17

A U (A ∩ B) = A
A Int (A U B) = A

Question 18

U

Answer 18

Union (or)

Question 19

∩

Answer 19

Intersection (and)

Question 20

∈

Answer 20

is an element of/belongs to

Question 21

⊂

Answer 21

Proper subset

Question 22

And

Answer 22

ʌ

Question 23

⊆

Answer 23

Subset

Question 24

Or

Answer 24

v

Question 25

Implies

Answer 25

=>

Question 26

{ }

Answer 26

Empty set/Null set

Question 27

△

Answer 27

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

Question 28

If and Only if

Answer 28

<=>

Question 29

Law of Double Negation (Laws of Logic)

Answer 29

¬¬ p 三 p

Question 30

It is not the case that / not

Answer 30

¬

Question 31

Or - form of an implication (Laws of Logic)

Answer 31

p → q 三 ¬ p v q

Question 32

Contrapositive form of an implication (Laws of Logic)

Answer 32

p → q 三 ¬ p → ¬ q

Question 33

De Morgan's Law (Laws of Logic)

Answer 33

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

Question 34

Rule for Direct Proof (Laws of Logic)

Answer 34

(p ʌ r) → q 三 r → (p → q)

Question 35

Rule for Proof by Contradiction (Laws of Logic)

Answer 35

(p ʌ ¬ q → o) 三 (p → q)

Question 36

Commutative Laws (Laws of Logic)

Answer 36

p v q 三 q v p p ʌ q 三 q ʌ p

Question 37

Associative Laws (Laws of Logic)

Answer 37

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

Question 38

Distributive Laws (Laws of Logic)

Answer 38

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)

Question 39

Idempotent Laws (Laws of Logic)

Answer 39

p v p 三 p p ʌ p 三 p

Question 40

Identity Laws (Laws of Logic)

Answer 40

p v o 三 p p ʌ I 三 p

Question 41

Inverse Laws (Laws of Logic)

Answer 41

p v ¬ p 三 I p ʌ ¬ p 三 o

Question 42

Domination Laws (Laws of Logic)

Answer 42

p v I 三 I p ʌ o 三 o

Question 43

Absorption Laws (Laws of Logic)

Answer 43

p v (p ʌ q) 三 p p ʌ (p v q) 三 p

Question 44

"o" (Laws of Logic)

Answer 44

Statement that is always false

Question 45

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

Answer 45

min (p,q)

Question 46

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

Answer 46

max (p,q)

Question 47

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

Answer 47

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

Question 48

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

Answer 48

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.

Question 49

Although

Answer 49

ʌ

Question 50

But

Answer 50

ʌ

Question 51

Even though

Answer 51

ʌ

Question 52

However

Answer 52

ʌ

Question 53

Unless

Answer 53

v

Question 54

When ........., then.......

Answer 54

→

Question 55

Provided that .......... , then .........

Answer 55

→

Question 56

Just in case that

Answer 56

<=>

Question 57

"I" (Laws of Logic)

Answer 57

A statement that is always true

Question 58

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

Answer 58

Tautology

Question 59

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

Answer 59

Contradiction

Question 60

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

Answer 60

Contingent

Question 61

Converse and Inverse are examples of _________.

Answer 61

Invalid Arguments

Question 62

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

Answer 62

Conditional

Question 63

Given p → q, the inverse would be _________

Answer 63

¬ p → ¬ q (Negation)

Question 64

Given p → q, the converse would be _________

Answer 64

q → p (Swap)

Question 65

Given p → q, the contrapositive would be _________

Answer 65

¬ q → ¬ p (Negation and Swap)

Question 66

[p ʌ (p → q)] → q (Rule of Inference)

Answer 66

Modus Ponens

Question 67

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

Answer 67

Law of Syllogism

Question 68

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

Answer 68

Modus Tollens

Question 69

[¬ p → 0] → p (Rule of Inference)

Answer 69

Rule of Contradiction

Question 69

(p ʌ q) → p (Rule of Inference)

Answer 69

Rule of Conjunctive Simplification

Question 69

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

Answer 69

Rule of Disjunctive Syllogism

Question 69

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

Answer 69

Rule of Conditional proof

Question 69

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

Answer 69

Rule for Proof by Cases

Question 69

p → p v q (Rule of Inference)

Answer 69

Rule of Disjunctive Amplification

Question 69

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

Answer 69

Rule of Constructive Dilemma

Question 69

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

Answer 69

Rule of Destructive Dilemma

Question 70

A - B is the same as

Answer 70

A Int B'