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2016年12月30日 · When you have the statement "q if p," it translates to "p implies q;" and this makes sense: q can only be true if p is true. Now, when I see the statement "p only if q," I simply see this as a stronger version of "q if p," and should thus be translated in …

2020年8月28日 · So this conditional statement is false -- there is a propositional universe in which the condition is true but the conclusion is false. We (up to fussiness about the distinction between formal propositional systems and the real world) live in such a universe. The conditional leads to wrong conclusions in that universe.

2020年1月25日 · It's prohibited when and only when the following statement is true: The person is a child and the person is drinking whiskey. Notice that the second statement describes exactly the opposite situation to the first statement. In other words, the second statement is true when and only when the first statement is false.

2015年12月27日 · In programming, often the value of True is also 1, and False is 0. This means that: (x>5)*4 will return 4 if x is greater than 5 (because (x>5)==1), else 0.

2016年5月10日 · The conditional of natural if-then reasoning is called the indicative conditional, but that can hardly be formalized given the vagueness of natural language and reasoning. Some approximation of it is given by the conditional in relevance logic, which demands in particular that the premise be relevant to the conclusion for the conditional to ...

2016年4月9日 · What the statement "If A then B" means in logic is that there is never a case where A is true and B is false. If A is true, then B will be true. Another way of saying that is that either B will be true or A will be false.

Maybe this comes down to my tenuous understanding of the conditional statement. Perhaps the reason I am misusing the conditional statement here and in other occasions is because it's definition is a bit weird to me. Like the conditional statement is basically only ever false when the hypothesis is true but the conclusion is false.

2016年9月6日 · My textbook states that for the conditional statement "p implies q", "p is a sufficient condition for q and q is a necessary condition for p." How is this so? One might be lead to believe that p is independent of q and that it is a necessary and sufficient condition for q, no?

2018年7月22日 · There are a lot of different hypotheses floating around. (You never have to prove that anything is true for a false value of a hypothesis, though. A false statement implies anything.) You have to prove the conclusion is true if the hypothesis is true, just as in the proof of every theorem. In this particular example, it's a proof by cases ...