I] Introduction Flashcards
Which type of value is assigned to a statement?
Truth (True or False)
How is written the negative statement?
¬A (none A)
How many possibilities is there for a 2 statements operator?
2^4
What is the symbol for “AND” operator?
A∧B
What does ∧ mean?
True if both are True, otherwise, it’s False
What is the symbol for the “OR” operator?
A∨B
What does ∨ mean?
True if one, at least, is True
What is the symbol for “Exclusive OR” / “XOR”
AwB
What does w mean?
True if ONLY one statement is True
What is the symbol for “equivalence”?
A < = > B
What does “A < = > B” mean?
True when both statement are the same value
What is the symbol for “implication”?
A=>B
What does A=>B mean?
True when B is True or both are False
What is “contraposition”?
A=>B is the same as (¬B)=>(¬A)
What is a “set”?
Collection (final or not) of elements.
How do you denote a set?
S={1,2,3,4}
What is the symbol for set inclusion?
x∈S
What is the symbol for a none-inclusion in a set?
x∉S
How do you write the “empty set”?
∅={ }
How do you write a “subset?
B⊂A
How do you write a none-subset?
B⊄A
How do you write the quantifier “for all”?
∀x∈S (All x that belong to S)
How do you write the quantifier “at least 1”?
∃x∈S (At least 1 x that belong to S)
How do you write a “union” of 2 sets?
A∪B
What does mean A∪B?
A∪B= {x⎪x∈A ∨ x∈B}
How do you write an “intersection” of 2 sets”?
A∩B
What does A∩B mean?
A∩B={x⎪x∈A ∧ x∈B}
A∪∅=?
A∪∅=A
A∪A=?
A∪A=A
If B⊂A, A∪B=?
A∪B=A
A∩∅=?
A∩∅=∅
A∩A=?
A∩A=A
If B⊂A, A∩B=?
A∩B=B
How do you write a “set minus”?
A∖B
What does mean “A∖B”?
A∖B = {x⎪x∈A ∧ x∉B}
How do you write a “set complement”?
A̅
What does mean “A̅”?
A̅= S∖A
∅̅=?
∅̅=S∖∅
∅̅=S
S̅=?
S̅=S∖S
S̅=∅
X̅̅=?
X̅̅=X
What is “commutativity”?
A∪B = B∪A A∩B = B∩A
What is “associativity”?
A∩(B∩C) = (A∩B)∩C A∪(B∪C) = (A∪B)∪C
What is a “neutral element”?
e✻a=a e is the neutral element
What are the “neutral elements” for ∪ and ∩?
S for ∩ (S∩A = A)
∅ for ∪ (∅∪A = A)
What is “involution”?
A̅̅ = A
What is “distributivity”?
A∩(B∪C) = (A∩B)∪(A∩C) A∪(B∩C) = (A∪B)∩(A∪C)
What are “duality equalities” / “De Morgan laws”?
(A∪B) bar = A̅∩B̅
(A∩B) bar = A̅∪B̅
