Difference between Boolean operator symbols for AND and OR

Question

I feel like an idiot for asking this because I SHOULD know the answer, but what is the difference between the Boolean logic operators for AND and OR? For instance, I know AND can have the symbols $\&$, $\land$, and ·. I also know OR can have the symbols $|$, $\lor$, and $+$. I'm just not quite sure what the differences are. Put another way, when is one used over another? Help clarifying this would be greatly appreciated. Thank you all!

Answer 1

The symbols $\land$ and $\lor$ are logical connectives. Their operands are statements that are either true or false.

The symbols $\cdot$ and $+$ are switching circuit theory connectives. Their operands are switches that are either open (infinite impedance) or closed (zero impedance).

Shannon (1938) noted that "the calculus of propositions" (or Huntington's (1904, 1933) "algebra of logic") had an equivalent interpretation in relay circuits.

Essentially, the two sets of symbols represent different things, but statements involving them are equivalent, so some people now use them interchangeably.

References:

• Huntington, E. V. (1904, July). Sets of independent postulates for the algebra of logic. Transactions of the American Mathematical Society, 5(3), 288-309.

• Huntington, E. V. (1933, January). New sets of independent postulates for the algebra of logic, with special reference to Whitehead and Russell's Principia Mathematica. Transactions of the American Mathematical Society, 35(1), 274-304.

• Shannon, C. E. (1938, December). A symbolic analysis of relay and switching circuits. Transactions of the American Institute of Electrical Engineers, 57(12), 713-723.