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ˇ“)
RE
(x, y)∈E2xRy⇒yRx xRy
yRx xRx
ˇ“)
PO∀(M, N )∈ P2MRN⇔
O, M, N
ˇ“)
E
ˇ“(
E F f ∈FE
RE xRy⇔f(x) = f(y)
RE
a∈E a f
f
EP(E)E
∀(A, B)∈ P(E)2, ARB⇔A=B A =B
ˇ“(
ER2// E
//
ˇ“
E x E P(E)
ARB⇔(x∈A∩B)∨(x∈A∩B)
ˇ“
RE6=∅x∈E˚x
xR(x, y)∈E2

xRy
˚x= ˚y
˚x∩˚y6=∅
x y
(x, y)∈E2˚x6= ˚y⇔˚x∩˚y=∅
RRxRy⇔xey=yex
Rx∈R˚x x R
ˇ“
R
aRb a3−b3=a−b
R
ˇ“
N×N(x, x0)R(y, y0)x+y0=x0+y
R(1; 2)
ˇ“
R2(x, y)R(z, t)⇔xy =zt
RR
xz ≥0
Rnn
RnRkk < n
Rnn≤6
E, F X =FE
f∼g⇐⇒ ∃ φ:F−→ F g =φ◦f,
f≡g⇐⇒ ∀x, y ∈E, f (x) = f(y)⇐⇒ g(x) = g(y).
f∼g⇒f≡g
f≡g f ∼g
F f
F f
E
E=F=N
E F f ∈FE
RE xRy⇔f(x) = f(y)
RE

a∈E a f
f
f
fRf(x) = x2−x a
fR2f(x, y) = x−y(a, b)∈R2
∼E A ⊂E s(A) = S
x∈A
˙x
A s(A)
s(s(A))
∀x∈E(x∈s(A)) ⇐⇒ ( ˙x∩s(A)6=∅)s(E\s(A))
sS
i∈I
Ai=S
i∈I
s(Ai)sT
i∈I
Ai⊂T
i∈I
s(Ai)
f
f:E→FS={X⊂E f−1(f(X)) = X}
A⊂E f−1(f(A)) ∈ S
S
X∈ S A⊂E X ∩A=∅X∩f−1(f(A)) = ∅
X Y ∈ S X Y \XS
ϕ:S −→ P(f(E))
A7−→ f(A)
E F f :E−→ F
RE(x, x0)∈E×E xRx0⇔f(x) = f(x0)
∼Zx∼y⇐⇒ x2≡y2[5]
RESF E ×F
(x, y)∼(x0, y0)⇐⇒ xRx0ySy0.
∼
φ:E×F−→ (E/R)×(F/S)
(x, y)7−→ ( ˙x, ˙y)
φ∼
X∪A=Y∪A
E A ⊂EP(E)
X∼Y⇐⇒ X∪A=Y∪A.

φ:P(E)−→ P(E\A)
X7−→ X\A
φ∼
EE
E F =EE
f∼g⇐⇒ ∃ n∈N∗fn=gn,
f≈g⇐⇒ ∃ m, n ∈N∗fn=gm,
f≡g⇐⇒ f(E) = g(E).
∼ ≈ ≡
f∈F f∼f≈f≡f∼ ≈ ≡
f∼f≈
≈ ∼
f g ∈f≈
f≡
R S E
∀x, y ∈E, xRy⇒xSy.
˙
SE/R˙x˙ S˙y⇐⇒ xSy
˙
S(E/R)/˙ SE/S
RE
xSy⇐⇒ (xRy yRx),
xTy⇐⇒ (xRy yRx).
S T
E F f ∈FE
RE xRy⇔f(x) = f(y)
RE
a∈E a f
f
f
fRf(x) = x2−x a
fR2f(x, y) = x−y(a, b)∈R2
E
x y z E
T[¬(xy)∧ ¬(yz)] ⇒ ¬(xz)
A(xy)⇒ ¬(yx)

E∼ 
∀(x, y)∈E2,(x∼y)⇔[¬(xy)∧ ¬(yx)]
∀(x, y)∈E2,(xy)⇔[(xy)∨(x∼y)]
E x y x ∼y
xy x y x y
x y
(xy),(yx),(x∼y)
∼
∀(x, y, z)∈E3,(xy)∧(y∼z)⇒(xz)
∀(x, y, z)∈E3,(x∼y)∧(yz)⇒(xz)