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ስዕል:Venn1010.svg

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One of 16 Venn diagrams, representing 2-ary Boolean functions like set operations and [[w:Logical corect 81 233 166 409 ¬A or ¬B rect 260 231 349 409 A or ¬B rect 393 230 481 409 ¬A or B rect 574 232 663 408 A or B rect 13 436 103 617 ¬B rect 147 438 235 617 ¬A rect 279 440 368 616 A xor B rect 375 440 464 617 A xnor B rect 507 439 595 617 A rect 639 438 732 617 B rect 79 647 168 826 ¬A and ¬B rect 260 647 349 826 A and ¬B rect 392 646 482 826 ¬A and B rect 574 646 663 826 A and B rect 327 853 417 1035 X and ¬X desc top-right </imagemap>

Operations and relations in set theory and logic

 
∅c		           
A = A
1111 1111
 
Ac  Bc		 true
A ↔ A		  
A  B		  
A  Bc		 AA
 		  
A  Bc
1110 0111 1110 0111
 
A  Bc		 ¬A  ¬B
A → ¬B		  
A  B		 A  B
A ← ¬B		  
Ac B		  
A B		 A¬B
 		  
A = Bc		 A¬B
 		  
A B
1101 0110 1011 1101 0110 1011
 
Bc		 A  ¬B
A ← B		  
A		 A  B
A ↔ ¬B		  
Ac		 ¬A  B
A → B		  
B		  
B = ∅		 AB
 		  
A = ∅c		 A¬B
 		  
A = ∅		 AB
 		  
B = ∅c
1100 0101 1010 0011 1100 0101 1010 0011
¬B
 		  
A  Bc		 A
 		  
(A  B)c		 ¬A
 		  
Ac  B		 B
 		 Bfalse
 		 Atrue
 		  
A = B		 Afalse
 		 Btrue
 
0100 1001 0010 0100 1001 0010
A  ¬B
 		  
Ac  Bc		 A  B
 		  
A  B		 ¬A  B
 		 AB
 
1000 0001 1000 0001
¬A  ¬B
 		  
∅		 A  B
 		  
A = Ac
0000 0000
false
A ↔ ¬A		 A¬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.



This work is ineligible for copyright and therefore in the public domain because it consists entirely of information that is common property and contains no original authorship.

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