I] Introduction

Question 1

Which type of value is assigned to a statement?

Answer 1

Truth (True or False)

Question 2

How is written the negative statement?

Answer 2

¬A (none A)

Question 3

How many possibilities is there for a 2 statements operator?

Answer 3

2^4

Question 4

What is the symbol for “AND” operator?

Answer 4

A∧B

Question 5

What does ∧ mean?

Answer 5

True if both are True, otherwise, it’s False

Question 6

What is the symbol for the “OR” operator?

Answer 6

A∨B

Question 7

What does ∨ mean?

Answer 7

True if one, at least, is True

Question 8

What is the symbol for “Exclusive OR” / “XOR”

Answer 8

AwB

Question 9

What does w mean?

Answer 9

True if ONLY one statement is True

Question 10

What is the symbol for “equivalence”?

Answer 10

A < = > B

Question 11

What does “A < = > B” mean?

Answer 11

True when both statement are the same value

Question 12

What is the symbol for “implication”?

Answer 12

A=>B

Question 13

What does A=>B mean?

Answer 13

True when B is True or both are False

Question 14

What is “contraposition”?

Answer 14

A=>B is the same as (¬B)=>(¬A)

Question 15

What is a “set”?

Answer 15

Collection (final or not) of elements.

Question 16

How do you denote a set?

Answer 16

S={1,2,3,4}

Question 17

What is the symbol for set inclusion?

Answer 17

x∈S

Question 18

What is the symbol for a none-inclusion in a set?

Answer 18

x∉S

Question 19

How do you write the “empty set”?

Answer 19

∅={ }

Question 20

How do you write a “subset?

Answer 20

B⊂A

Question 21

How do you write a none-subset?

Answer 21

B⊄A

Question 22

How do you write the quantifier “for all”?

Answer 22

∀x∈S (All x that belong to S)

Question 23

How do you write the quantifier “at least 1”?

Answer 23

∃x∈S (At least 1 x that belong to S)

Question 24

How do you write a “union” of 2 sets?

Answer 24

A∪B

Question 25

What does mean A∪B?

Answer 25

A∪B= {x⎪x∈A ∨ x∈B}

Question 26

How do you write an “intersection” of 2 sets”?

Answer 26

A∩B

Question 27

What does A∩B mean?

Answer 27

A∩B={x⎪x∈A ∧ x∈B}

Question 28

A∪∅=?

Answer 28

A∪∅=A

Question 29

A∪A=?

Answer 29

A∪A=A

Question 30

If B⊂A, A∪B=?

Answer 30

A∪B=A

Question 31

A∩∅=?

Answer 31

A∩∅=∅

Question 32

A∩A=?

Answer 32

A∩A=A

Question 33

If B⊂A, A∩B=?

Answer 33

A∩B=B

Question 34

How do you write a “set minus”?

Answer 34

A∖B

Question 35

What does mean “A∖B”?

Answer 35

A∖B = {x⎪x∈A ∧ x∉B}

Question 36

How do you write a “set complement”?

Answer 36

A̅

Question 37

What does mean “A̅”?

Answer 37

A̅= S∖A

Question 38

∅̅=?

Answer 38

∅̅=S∖∅

∅̅=S

Question 39

S̅=?

Answer 39

S̅=S∖S

S̅=∅

Question 40

X̅̅=?

Answer 40

X̅̅=X

Question 41

What is “commutativity”?

Answer 41

A∪B = B∪A
A∩B = B∩A

Question 42

What is “associativity”?

Answer 42

A∩(B∩C) = (A∩B)∩C
A∪(B∪C) = (A∪B)∪C

Question 43

What is a “neutral element”?

Answer 43

e✻a=a e is the neutral element

Question 44

What are the “neutral elements” for ∪ and ∩?

Answer 44

S for ∩ (S∩A = A)

∅ for ∪ (∅∪A = A)

Question 45

What is “involution”?

Answer 45

A̅̅ = A

Question 46

What is “distributivity”?

Answer 46

A∩(B∪C) = (A∩B)∪(A∩C)
A∪(B∩C) = (A∪B)∩(A∪C)

Question 47

What are “duality equalities” / “De Morgan laws”?

Answer 47

(A∪B) bar = A̅∩B̅

(A∩B) bar = A̅∪B̅