The following is the truth-table describing the definitions which allow us to establish truth values to composite formulae or molecules, which is nothing new:
I had an idea about playing with the truth values to switch up their order to see how they relate. So for instance if we take a look at p * q, the truth values of it are in the order(from top to bottom) that is (T, F, F, F). Which composite formula would have the truth values of the reverse order of p*q, which would be (F ,F ,F ,T)? Further could we find something interesting, like shortcuts, if we ask the same question about p v q, p$\rightarrow$ q etc.
I am not asking for the negation of the values, Im asking if the order f the truth values in the tables was "reversed": made bottom to top from the original top to bottom. Though you could reverse the values and then negate to get the orginal formula but that I already know
If this is already done, please refer me to some site or source where it is discussed? Thanks in advance.
There are 16 possible binary logic operators (that is, operators like ⋀ and ⋁ that return a true or false value based on two inputs). 4 of them depend on one value while completely ignoring the other, while 2 more (always true and always false) ignore both values. So only 10 of the operators are of any interest. These 10 have been given a variety of names, but one set consists of ("or", "and", "nor" (the operator in your example), "nand", "if", "onlyif", "nif", "nonlyif", "equals", and "nequals"). "if", or "p if q" or "q implies p" is equivalent to (p ⋁ ~q). I'll leave it to you to figure out the rest.