User:Hexadecimal

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[edit] Logical connectives and hexadecimal numbers

false false false false 0 0 0 0
p AND q = p --\--> ¬q = ¬p <--/-- q = ¬p NOR ¬q 0 0 0 1
p --\--> q = p AND ¬q = ¬p NOR q = ¬p <--/-- ¬q 0 0 1 0
p 0 0 1 1
p <--/-- q = p NOR ¬q = ¬p AND q = ¬p --\--> ¬q 0 1 0 0
q 0 1 0 1
p XOR q = p XNOR ¬q = ¬p XNOR q = ¬p XOR ¬q 0 1 1 0
p OR q = p <----- ¬q = ¬p -----> q = ¬p NAND ¬q 0 1 1 1
p NOR q = p <--/-- ¬q = ¬p --\--> q = ¬p AND ¬q 1 0 0 0
p XNOR q = p XOR ¬q = ¬p XOR q = ¬p XNOR ¬q 1 0 0 1
¬q 1 0 1 0
p <----- q = p OR ¬q = ¬p NAND q = ¬p -----> ¬q 1 0 1 1
¬p 1 1 0 0
p -----> q = p NAND ¬q = ¬p OR q = ¬p <----- ¬q 1 1 0 1
p NAND q = p -----> ¬q = ¬p <----- q = ¬p OR ¬q 1 1 1 0
true true true true 1 1 1 1
0hex = 0dec = 0oct 0 0 0 0
1hex = 1dec = 1oct 0 0 0 1
2hex = 2dec = 2oct 0 0 1 0
3hex = 3dec = 3oct 0 0 1 1
4hex = 4dec = 4oct 0 1 0 0
5hex = 5dec = 5oct 0 1 0 1
6hex = 6dec = 6oct 0 1 1 0
7hex = 7dec = 7oct 0 1 1 1
8hex = 8dec = 10oct 1 0 0 0
9hex = 9dec = 11oct 1 0 0 1
Ahex = 10dec = 12oct 1 0 1 0
Bhex = 11dec = 13oct 1 0 1 1
Chex = 12dec = 14oct 1 1 0 0
Dhex = 13dec = 15oct 1 1 0 1
Ehex = 14dec = 16oct 1 1 1 0
Fhex = 15dec = 17oct 1 1 1 1





p AND q 0 0 0 1
p AND ¬q 0 0 1 0
¬p AND q 0 1 0 0
¬p AND ¬q 1 0 0 0
p OR q 0 1 1 1
p OR ¬q 1 0 1 1
¬p OR q 1 1 0 1
¬p OR ¬q 1 1 1 0





The logical connectives ordered by inclusion in a Hasse diagram ...
The logical connectives ordered by inclusion in a Hasse diagram ...
   
... forming a rhombic dodecahedron, the tesseracts vertex first shadow
... forming a rhombic dodecahedron, the tesseracts vertex first shadow
1100: ¬p
1100: ¬p
1101: ¬p OR q = p→q
1101: ¬p OR q = p→q
1110: ¬p OR ¬q
1110: ¬p OR ¬q
1111: tautology
1111: tautology
1000: ¬p AND ¬q
1000: ¬p AND ¬q
1001: p XNOR q
1001: p XNOR q
1010: ¬q
1010: ¬q
1011: p OR ¬q = p←q
1011: p OR ¬q = p←q
0100: ¬p AND q
0100: ¬p AND q
0101: q
0101: q
0110: p XOR q
0110: p XOR q
0111: p OR q
0111: p OR q
0000: contradiction
0000: contradiction
0001: p AND q
0001: p AND q
0010: p AND ¬q
0010: p AND ¬q
0011: p
0011: p

[edit] Syllogisms

The fifteen "strong" Syllogisms of Aristotle - a bijection with a four element sets non empty subsets?


000L: Modus Darii00L0: Modus Datisi00LL: Modus Ferio0L00: Modus Disamis0L0L: Modus Festino0LL0: Modus Baroco0LLL: Modus CelarentL000: Modus DimatisL00L: Modus BocardoL0L0: Modus FerisonL0LL: Modus CesareLL00: Modus FresisonLL0L: Modus CamestresLLL0: Modus CalemesLLLL: Modus Barbara

[edit] Musical scales

Circle of fifth (How we use to think it)
Circle of fifth (How we use to think it)


Spiral of fifth (How it really is)
Spiral of fifth (How it really is)