# Can multiplication and division be treated as logical operations?

A few of my friends and I were playing around with math (more specifically, why (-1)(-1)=1) and we figured out that multiplication (with regards to signs) was an "nxor" operation (I.E. If we treat "1" as "true" and "-1" as "false," than the values of multiplication, again with regards to signs, are the same as the "nxor" operation.) Now, we've begun thinking about redefining multiplication as other logical operations (For example: under "and" (-1)(-1)=-1) My questions are these: is this line of thought similar to any current area of mathematical research? If so, where can I go to find more information on it. I am especially interested in any proven theorems or open conjectures on this topic.

• You may want to take a look at truth-tables. Note, though, that any resemblance that your logic functions have to arithmetic functions depends on how you choose to represent "true" and "false". In your case "1" and "-1". Under your interpretation "and" is the same as "min" and "or" is the same as "max". May 10, 2016 at 15:59
• more conventional is 1 for true and 0 for false, and multiplication for "and". May 10, 2016 at 16:03