Conversely, if the result is false that means In simpler words, the true values in the truth table are for the Your assumption that $A$ implies $B$ is violated (or is not correct). Situations) that results in a false value of $(\lnot A \lor B)$ then Truth table represents is the fact that if you have a data set (or True if you use the equivalent $(\lnot A \lor B)$ logic. Here is that this truth table is not about when the result will be My conclusion and probably the mistake I've been making to understand However, if we were not correct in making that earlier assumption, and there is another State which has a city of Los Angeles, in that case the test (~A V B) will result in false thus proving that the assumption "City=Los Angeles implies State=CA" is wrong. Now, based on our assumption, whenever we find an address with city of Los Angeles, we can infer that the State must be California (if A is true it will imply that B is also true). So we setup two tests 'A' (City=Los Angeles) and 'B' (State=CA). Let's say we have an assumption that the State of California is the only State with a city named Los Angeles. And now as I read it, I guess, I'm stating the obvious but let's try it with an example. Conversely, if the result is false that means that the statement A implies B is also false. In simpler words, the true values in the truth table are for the statement A implies B. What this truth table represents is the fact that if you have a data set (or situations) that results in a false value of (~A V B) then your assumption that A implies B is violated (or is not correct). My conclusion and probably the mistake I've been making to understand here is that this truth table is not about when the result will be true if you use the equivalent (~A V B) logic. Second one implies, to me anyway, that given A implies B, the truth ofī rests upon the truth of A, B is false, A is True, which cannot be, Now, my confusion here is regarding why A->B given A is false, and B In the truth table, where A->B we obtain this result: A | B |A->B So, you'll probably have an idea of where my confusion lies right from p implies q) True if both p and qĪre False? I have just started studying implication in mathematics. Here's what I came up with and would like folks to review and comment. Although all the answers are accurate and correct in their own way of explaining (or went above my head), those still didn't "click" for me so I kept trying to find a more specific example. These trademark holders are not affiliated with question that has bothered me for a while has been answered and closed here ( Implication in mathematics - How can A imply B when A is False?) and probably many other posts.
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