User:Paul August/Subpage 16

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[edit] Other notation

The operators of Boolean algebra may be represented in various ways. Often they are simply written as AND, OR and NOT. In describing circuits, NAND (NOT AND), NOR (NOT OR) and XOR (eXclusive OR) may also be used. Mathematicians, engineers, and programmers often use + for OR and · for AND (since in some ways those operations are analogous to addition and multiplication in other algebraic structures and this notation makes it very easy to get sum of products form for people who are familiar with normal algebra) and represent NOT by a line drawn above the expression being negated.

The above uses the "join"\lor and "meet" \land for the binary operators and \lnot for the unary operator and 0 and 1 for the least and greatest elements.


order theoretic set theoretic logical algebraic
∨ join ∪ union or disjunction + plus
∧ meet ∩ intersection and conjunction · times
¬ complement _C complement not negation − minus
0 bottom ∅ empty set 0 zero
1 top U universe 1 one
∨ Δ symmetric
difference		 xor exclusive
disjunction
≤ less than
or equal		 ⊆ inclusion ≤ less than
or equal