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Discreet Mathematics and it's applications 4th Edition: Set Theory Symbols Chapter 1
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Gravity
Key Concepts:
Terms in this set (83)
∼p
not p
p ∧ q
p and q
p ∨ q
p or q
p ⊕ q or p XOR q
p or q but not both p and q
P ≡ Q
p is logically equivalent to q
p → q
if p then q
p ↔ q
p if and only if q
∴
therefore
P(x)
predicate in x
P(x) ⇒ Q(x)
every element in the truth set for P(x) is in the truth set for Q(x)
P(x) ⇔ Q(x)
P(x) and Q(x) have identical truth sets
∀
for all
∃
there exists

Sheffer stroke
NOT gate
NOTGate
NOTGate
NOTGate
ANDGate
AndGate
ORGate
ORGate
NANDGate
NANDGate
NORGate
NORGate
↓
Peirce arrow
n2
number written in binary notation
n10
number written in decimal notation
n16
number written in hexadecimal notation
d  n
d divides n
d / n
d does not divide n
n div d
the integer quotient of n divided by d
n mod d
the integer remainder of n divided by d
_x_
the floor of x
_ _
x
the ceiling of x
x
absolute value of x
gcd(a, b)
the greatest common divisor of a and b
x := e
x is assigned the value e
...
and so forth
n
Σak
k=m
the summation from k equals m to n of ak
n
Πak
k=m
the product from k equals m to n of ak
n!
n factorial
a ∈ A
a is an element of A
a ∈/ A
a is not an element of A
{a1, a2,..., an }
the set with elements a1, a2,..., an
{x ∈ D  P(x)}
the set of all x in D for which P(x) is true
R, R−, R+, Rnonneg
the sets of all real numbers, negative real numbers, positive real numbers, and nonnegative real numbers
Z, Z−, Z+, Znonneg
the sets of all integers, negative integers, positive integers, and nonnegative integers
Q, Q−, Q+, Qnonneg
the sets of all rational numbers, negative rational numbers, positive rational numbers, and nonnegative rational numbers
N
the set of natural numbers
A ⊆ B
A is a subset of B
A ⊆/ B
A is not a subset of B
A = B
A equals B
A ∪ B
The union of A and B.
A ∩ B
Intersection: in both A and B
B − A
The difference of B minus A
Ac
the complement of A
(x, y)
ordered pair
(x1, x2,..., xn )
ordered ntuple
A × B
the Cartesian product of A and B
A1 × A2 ×···× An
the Cartesian product of A1, A2,..., An
∅
the empty set
P(A)
the power set of A
N(A)
the number of elements in set A
P(A)
the probability of a set A
P(n,r)
the number of rpermutations of a set with n elements
(n
r)
n choose r, the number of rcombinations of a set of n elements, the number of relement subsets of a set of n elements
[xi1 , xi2 ,..., xir ]
multiset of size r
P(A  B)
the probability of A given B
f : X → Y
f is a function from X to Y
f (x)
the value of f at x
f
x→y
f sends x to y
f (A)
the image of A
f −1(C)
the inverse image of C
Ix
the identity function on X
b^x or exp b(x)
b raised to the power x
log b(x)
logarithm with base b of x
F−1
the inverse function of F
f ◦ g
the composition of g and f
x ∼= y
x is approximately equal to y
O( f (x))
bigO of f of x
Ω( f (x))
bigOmega of f of x
Θ( f (x))
bigTheta of f of x
x R y
x is related to y by R
R−1
the inverse relation of R
m ≡ n (mod d)
m is congruent to n modulo d
[a]
the equivalence class of a
x ≤ y
x is related to y by a partial order relation ≤
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