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A
⊕
B
=
(
A
c
⊖
B
s
)
c
Search
Returned 72 matches (100 formulae, 60 docs)
Lookup 2.050 ms, Re-ranking 221.987 ms
Found 20787 tuple postings, 16604 formulae, 6491 documents
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[ documents ]
[ documents-by-formula ]
Doc 1
1.0000
3.6723
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Mathematical_morphology.html
A
⊕
B
=
(
A
c
⊖
B
s
)
c
A
∙
B
=
(
A
c
∘
B
s
)
c
A
∙
B
=
(
A
c
∘
B
s
)
c
A
∘
B
=
(
A
⊖
B
)
⊕
B
A
∙
B
=
(
A
⊕
B
)
⊖
B
A
⊕
B
=
⋃
b
∈
B
A
b
(
A
⊖
B
)
⊖
C
=
A
⊖
(
B
⊕
C
)
(
A
⊕
B
)
⊆
C
(
A
⊕
B
)
⊕
C
=
A
⊕
(
B
⊕
C
)
Doc 2
0.6458
1.2143
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Opening_(morphology).html
A
∙
B
=
(
A
c
∘
B
s
)
c
A
∘
B
=
(
A
⊖
B
)
⊕
B
,
(
A
∘
B
)
∘
B
=
A
∘
B
Doc 3
0.4271
0.7819
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Union_(set_theory).html
A
∪
B
=
(
A
C
∩
B
C
)
C
A
∩
(
B
∪
C
)
=
(
A
∩
B
)
∪
(
A
∩
C
)
A
∪
(
B
∩
C
)
=
(
A
∪
B
)
∩
(
A
∪
C
)
Doc 4
0.3368
0.4421
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Closing_(morphology).html
A
∙
B
=
(
A
⊕
B
)
⊖
B
,
(
A
∙
B
)
∙
B
=
A
∙
B
Doc 5
0.3256
2.6767
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/De_Morgan's_laws.html
A
c
∪
B
c
⊆
(
A
∩
B
)
c
A
c
∪
B
c
⊆
(
A
∩
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)
c
A
c
∪
B
c
⊆
(
A
∩
B
)
c
x
∈
(
A
∩
B
)
c
x
∈
(
A
∩
B
)
c
x
∈
(
A
∩
B
)
c
x
∉
(
A
∩
B
)
c
x
∉
(
A
∩
B
)
c
x
∈
(
A
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B
)
c
)
(
A
∪
B
)
c
=
A
c
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B
c
(
A
∩
B
)
c
=
A
c
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B
c
(
A
∩
B
)
c
=
A
c
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B
c
(
A
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c
⊆
A
c
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c
(
A
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c
⊆
A
c
∪
B
c
(
A
∩
B
)
c
⊆
A
c
∪
B
c
Doc 6
0.2857
1.4531
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Symmetric_difference.html
A
∪
B
=
(
A
△
B
)
△
(
A
∩
B
)
A
△
B
=
(
A
∪
B
)
∖
(
A
∩
B
)
,
A
△
B
=
(
A
∖
B
)
∪
(
B
∖
A
)
,
A
△
B
=
A
c
△
B
c
A
∩
(
B
△
C
)
=
(
A
∩
B
)
△
(
A
∩
C
)
,
A
⊕
B
.
A
⊖
B
.
Doc 7
0.2857
0.7298
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Ring_of_sets.html
A
△
B
=
(
A
∖
B
)
∪
(
B
∖
A
)
A
∪
B
=
(
A
△
B
)
△
(
A
∩
B
)
A
∖
B
=
A
△
(
A
∩
B
)
.
A
∩
B
=
A
∖
(
A
∖
B
)
.
Doc 8
0.2857
0.2857
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Linear_logic.html
A
≡
B
=
(
A
⊸
B
)
&
(
B
⊸
A
)
Doc 9
0.2857
0.2857
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Jaccard_index.html
A
△
B
=
(
A
∪
B
)
-
(
A
∩
B
)
Doc 10
0.2812
0.7165
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Two-element_Boolean_algebra.html
A
⋅
B
=
A
¯
+
B
¯
¯
A
+
B
=
A
¯
⋅
B
¯
¯
.
A
+
(
B
⋅
C
)
=
(
A
+
B
)
⋅
(
A
+
C
)
.
Doc 11
0.2812
0.2812
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Context-free_language.html
A
∩
B
=
A
¯
∪
B
¯
¯
Doc 12
0.2689
0.2689
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Set_(mathematics).html
A
Δ
B
=
(
A
∖
B
)
∪
(
B
∖
A
)
.
Doc 13
0.2667
0.2667
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Hit-or-miss_transform.html
A
⊙
B
=
(
A
⊖
C
)
∩
(
A
c
⊖
D
)
Doc 14
0.2316
0.2316
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Functional_completeness.html
A
∨
B
:=
(
A
→
B
)
→
B
.
Doc 15
0.2188
0.8812
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/List_of_logic_systems.html
B
→
(
A
∨
B
)
B
→
(
A
∨
B
)
A
→
(
B
→
(
A
∧
B
)
)
A
→
(
B
→
(
A
∧
B
)
)
(
A
↔
B
)
→
(
A
→
B
)
Doc 16
0.2188
0.3726
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Schnirelmann_density.html
A
⊕
B
=
𝒩
.
A
⊕
B
Doc 17
0.2110
0.2110
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Generalized_method_of_moments.html
I
-
B
=
(
I
-
B
)
(
I
-
B
)
′
Doc 18
0.2095
0.2095
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/E7_(mathematics).html
A
∘
B
=
(
A
B
+
B
A
)
/
2
Doc 19
0.2056
0.2056
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Hadamard_product_(matrices).html
A
∘
(
B
∘
C
)
=
(
A
∘
B
)
∘
C
,
Doc 20
0.2000
0.9327
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/XOR_swap_algorithm.html
A
⊕
B
=
B
⊕
A
A
⊕
B
A
⊕
B
(
A
⊕
B
)
⊕
A
=
A
⊕
(
A
⊕
B
)
=
(
A
⊕
A
)
⊕
B
(
A
⊕
B
)
⊕
B
=
A
⊕
(
B
⊕
B
)
(
A
⊕
B
)
⊕
C
=
A
⊕
(
B
⊕
C
)
Doc 21
0.1964
0.1964
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Monoidal_t-norm_logic.html
A
↔
B
≡
(
A
→
B
)
∧
(
B
→
A
)
Doc 22
0.1964
0.1964
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/T-norm_fuzzy_logics.html
A
↔
B
≡
(
A
→
B
)
∧
(
B
→
A
)
Doc 23
0.1964
0.1964
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/BL_(logic).html
A
↔
B
≡
(
A
→
B
)
∧
(
B
→
A
)
Doc 24
0.1935
0.1935
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Reaction_rate.html
A
+
B
⇌
|
A
⋯
B
|
‡
→
P
Doc 25
0.1818
0.1818
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Probability_axioms.html
P
(
B
∖
(
A
∩
B
)
)
Doc 26
0.1786
0.1786
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Duality_(mathematics).html
(
A
c
)
c
=
A
Doc 27
0.1774
0.9085
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Algebra_of_sets.html
A
∩
(
B
∪
C
)
=
(
A
∩
B
)
∪
(
A
∩
C
)
A
∪
(
B
∩
C
)
=
(
A
∪
B
)
∩
(
A
∪
C
)
(
A
∪
B
)
C
=
A
C
∩
B
C
(
A
∩
B
)
C
=
A
C
∪
B
C
A
∩
(
A
∪
B
)
=
A
A
∪
(
A
∩
B
)
=
A
A
∩
B
=
A
∖
(
A
∖
B
)
Doc 28
0.1707
0.1707
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Activity_selection_problem.html
B
=
(
A
∖
{
k
}
)
∪
{
1
}
Doc 29
0.1707
0.1707
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/Computron_tube.html
S
=
(
A
*
B
)
+
C
+
D
Doc 30
0.1695
0.4227
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Complement_(set_theory).html
(
A
c
)
c
=
A
.
(
A
∪
B
)
c
=
A
c
∩
B
c
.
(
A
∩
B
)
c
=
A
c
∪
B
c
.
Doc 31
0.1679
0.6258
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Cartesian_product.html
A
×
(
B
∖
C
)
=
(
A
×
B
)
∖
(
A
×
C
)
,
A
×
(
B
∩
C
)
=
(
A
×
B
)
∩
(
A
×
C
)
,
A
×
(
B
∪
C
)
=
(
A
×
B
)
∪
(
A
×
C
)
,
(
A
×
B
)
c
=
(
A
c
×
B
c
)
∪
(
A
c
×
B
)
∪
(
A
×
B
c
)
.
Doc 32
0.1667
0.1667
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/XOR_gate.html
A
⋅
B
¯
+
A
¯
⋅
B
≡
(
A
+
B
)
⋅
Doc 33
0.1651
0.1651
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Pfaffian.html
A
1
⊕
A
2
=
[
A
1
0
0
A
2
]
,
Doc 34
0.1647
0.1647
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Spherical_trigonometry.html
2
S
=
(
A
+
B
+
C
)
Doc 35
0.1647
0.1647
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Crossed_ladders_problem.html
(Eq. 1)
A
B
=
h
(
A
+
B
)
Doc 36
0.1609
0.1609
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Amagat's_law.html
B
1
,
2
=
(
B
1
+
B
2
)
/
2
Doc 37
0.1538
0.7608
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Exclusive_or.html
A
⊕
B
A
⊕
B
A
⊕
B
A
⊕
B
(
A
⊕
B
)
Doc 38
0.1538
0.4615
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Direct_sum.html
A
⊕
B
A
⊕
B
A
⊕
B
Doc 39
0.1538
0.2967
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Logic_gate.html
A
⊕
B
A
⊕
B
¯
Doc 40
0.1538
0.1538
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Carry-lookahead_adder.html
A
⊕
B
Doc 41
0.1538
0.1538
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Direct_sum_of_modules.html
A
⊕
B
Doc 42
0.1522
0.1522
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Geometric_calculus.html
𝒫
B
(
A
)
=
(
A
⋅
B
-
1
)
B
Doc 43
0.1489
0.2289
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Dilation_(morphology).html
A
⊕
B
=
⋃
b
∈
B
A
b
.
(
A
⊕
B
)
⊕
C
=
A
⊕
(
B
⊕
C
)
Doc 44
0.1474
0.1474
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/State-space_representation.html
𝐱
˙
(
t
)
=
(
A
+
B
K
)
𝐱
(
t
)
Doc 45
0.1455
0.7273
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Logical_conjunction.html
(
A
and
B
)
(
A
and
B
)
(
A
and
B
)
(
A
and
B
)
(
A
and
B
)
Doc 46
0.1455
0.2396
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Logical_biconditional.html
(
A
↔
B
)
A
↔
B
⇔
¬
(
A
⊕
B
)
Doc 47
0.1455
0.1455
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Tautology_(logic).html
(
A
∧
B
)
Doc 48
0.1455
0.1455
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Comma_category.html
(
A
↓
B
)
Doc 49
0.1443
0.2887
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Geometric_algebra.html
𝒫
B
(
A
)
=
(
A
⌟
B
-
1
)
⌟
B
𝒫
B
(
A
)
=
(
A
⌟
B
-
1
)
⌟
B
Doc 50
0.1429
0.1429
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Intuitionistic_logic.html
(
A
∧
B
)
*
Doc 51
0.1414
0.1414
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Lamé_function.html
d
2
y
d
x
2
=
(
A
+
B
\weierp
(
x
)
)
y
Doc 52
0.1400
0.1400
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Erosion_(morphology).html
(
A
⊖
B
)
⊖
C
=
A
⊖
(
B
⊕
C
)
Doc 53
0.1324
0.1324
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Q-Vandermonde_identity.html
(
A
+
B
)
m
(
A
+
B
)
n
Doc 54
0.1296
0.1296
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Damping.html
x
(
t
)
=
(
A
+
B
t
)
e
-
ω
0
t
Doc 55
0.1236
0.1236
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Feynman_parametrization.html
u
=
(
z
-
B
)
/
(
A
-
B
)
Doc 56
0.1228
0.1228
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Multivariate_mutual_information.html
A
~
=
(
A
~
∩
B
~
)
∪
(
A
~
\
B
~
)
Doc 57
0.1143
0.2286
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Homotopy_type_theory.html
(
A
=
B
)
→
(
A
≃
B
)
(
A
=
B
)
≃
(
A
≃
B
)
Doc 58
0.1127
0.2254
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Combinational_logic.html
A
+
(
A
⋅
B
)
=
A
A
⋅
(
A
+
B
)
=
A
Doc 59
0.1081
0.2162
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Natural_deduction.html
A
prop
B
prop
(
A
∧
B
)
prop
∧
F
A
true
B
true
(
A
∧
B
)
true
∧
I
Doc 60
0.1037
0.1037
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Adder_(electronics).html
C
o
u
t
=
(
A
⋅
B
)
+
(
C
i
n
⋅
(
A
⊕
B
)
)