Berkas:Venn0001.svg

Ukuran pratayang PNG ini dari berkas SVG ini: 384 × 280 piksel Resolusi lainnya: 320 × 233 piksel | 640 × 467 piksel | 1.024 × 747 piksel | 1.280 × 933 piksel | 2.560 × 1.867 piksel.

Ukuran asli (Berkas SVG, secara nominal 384 × 280 piksel, besar berkas: 3 KB)

Berkas ini berasal dari Wikimedia Commons dan mungkin digunakan oleh proyek-proyek lain. Deskripsi dari halaman deskripsinya ditunjukkan di bawah ini.

Ringkasan

Deskripsi

English: One of 16 Venn diagrams, representing 2-ary Boolean functions like set operations and logical connectives:

Operations and relations in set theory and logic

∅^c

A = A

A^c

\scriptstyle \cup

B^c

true
^{A ↔ A}

A

\scriptstyle \cup

B

A

\scriptstyle \subseteq

B^c

A

\scriptstyle \Leftrightarrow

A

\scriptstyle \supseteq

B^c

A

\scriptstyle \cup

B^c

¬A

\scriptstyle \lor

¬B
^{A → ¬B}

A

\scriptstyle \Delta

B

A

\scriptstyle \lor

B
^{A ← ¬B}

A^c

\scriptstyle \cup

B

A

\scriptstyle \supseteq

B

A

\scriptstyle \Rightarrow

¬B

A = B^c

A

\scriptstyle \Leftarrow

¬B

A

\scriptstyle \subseteq

B

B^c

A

\scriptstyle \lor

¬B
^{A ← B}

A

\scriptstyle \oplus

B
^{A ↔ ¬B}

A^c

¬A

\scriptstyle \lor

B
^{A → B}

B

B = ∅

A

\scriptstyle \Leftarrow

B

A = ∅^c

A

\scriptstyle \Leftrightarrow

¬B

A = ∅

A

\scriptstyle \Rightarrow

B

B = ∅^c

¬B

A

\scriptstyle \cap

B^c

A

(A

\scriptstyle \Delta

B)^c

¬A

A^c

\scriptstyle \cap

B

\scriptstyle \Leftrightarrow

false

A

\scriptstyle \Leftrightarrow

true

A = B

A

\scriptstyle \Leftrightarrow

false

B

\scriptstyle \Leftrightarrow

true

A

\scriptstyle \land

¬B

A^c

\scriptstyle \cap

B^c

A

\scriptstyle \leftrightarrow

B

A

\scriptstyle \cap

B

¬A

\scriptstyle \land

B

A

\scriptstyle \Leftrightarrow

B

¬A

\scriptstyle \land

¬B

∅

A

\scriptstyle \land

B

A = A^c

false
^{A ↔ ¬A}

A

\scriptstyle \Leftrightarrow

¬A

These sets (statements) have complements (negations).
They are in the opposite position within this matrix.

These relations are statements, and have negations.
They are shown in a separate matrix in the box below.

more relations

The operations, arranged in the same matrix as above. The 2x2 matrices show the same information like the Venn diagrams. (This matrix is similar to this Hasse diagram.) In set theory the Venn diagrams represent the set, which is marked in red.	These 15 relations, except the empty one, are minterms and can be the case. The relations in the files below are disjunctions. The red fields of their 4x4 matrices tell, in which of these cases the relation is true. (Inherently only conjunctions can be the case. Disjunctions are true in several cases.) In set theory the Venn diagrams tell, that there is an element in every red, and there is no element in any black intersection.
Negations of the relations in the matrix on the right. In the Venn diagrams the negation exchanges black and red. In set theory the Venn diagrams tell, that there is an element in one of the red intersections. (The existential quantifications for the red intersections are combined by or. They can be combined by the exclusive or as well.)	Relations like subset and implication, arranged in the same kind of matrix as above. In set theory the Venn diagrams tell, that there is no element in any black intersection.

Tanggal

22 Januari 2008

Sumber

Karya sendiri

Pembuat

Watchduck

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	Tanggal/Waktu	Miniatur	Dimensi	Pengguna	Komentar
terkini	23 Januari 2025 22.05		384 × 280 (3 KB)	wikimediacommons>Watchduck	correct size

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Berkas:Venn0001.svg

Ringkasan

Operations and relations in set theory and logic

Lisensi

Captions

Items portrayed in this file

menggambarkan

ukuran data

2.908 Bita

tinggi

280 piksel

lebar

384 piksel

tipe media

image/svg+xml

checksum ^Inggris

a85bb40a017725cd08586a1c770f055653854c0b

Riwayat berkas

Penggunaan berkas

Menu navigasi

Berkas:Venn0001.svg

Ringkasan

Operations and relations in set theory and logic

Lisensi

Captions

Items portrayed in this file

menggambarkan

ukuran data

2.908 Bita

tinggi

280 piksel

lebar

384 piksel

tipe media

image/svg+xml

checksum Inggris

a85bb40a017725cd08586a1c770f055653854c0b

Riwayat berkas

Penggunaan berkas

Menu navigasi

Pencarian

checksum ^Inggris