2023年7月1日 · 在学习蕴含 (implication)这个命题逻辑的时候，我们会看到下面的真值表 (truth table)。 对于真值表的第一行，第二行和第四行大多数人都没有问题，但是第三行就有点难理解，所以我查阅了一下英文对于蕴含的定义。 p → q is a conditional statement, it is the proposition "if p, then q". 看到conditional statement对于学过编程的人来说一下子就条件反射，conditional statement不就是if-else吗？ 所以我用下面的 伪代码 来模拟上面的命题。

2021年9月19日 · What this truth table represents is the fact that if you have a data set (or situations) that results in a false value of $(\lnot A \lor B)$ then your assumption that $A$ implies $B$ is violated (or is not correct). In simpler words, the true values in the truth table are for the statement “ $A$ implies $B$ ”.

Let 𝔹 = {0, 1}, where 0 is interpreted as the logical value false and 1 is interpreted as the logical value true. The truth table shows the ordered triples of a triadic relation L ⊆ 𝔹 × 𝔹 × 𝔹 that is defined as follows:

Here is the truth table for implies, also called material implication, (for which the symbol is \(\rightarrow \)):

2009年11月30日 · Judging from the truth tables, it is possible to infer the value of a=>b only for a=1 and b=0. In this case the value of a=>b is 0. For the rest of values (a,b), the value of a=>b is undefined: both (a=>b)=0 ("a doesn't imply b") and (a=>b)=1 ("a implies b") are possible:

Here's the table for logical implication: To understand why this table is the way it is, consider the following example: "If you get an A, then I'll give you a dollar." The statement will be true if I keep my promise and false if I don't. Suppose it's true that you get …

Basic Logic - The Implication Operator. In binary logic, we know about operators such as AND, OR, NOT. Another operator that is important in logic and in test design is the implies operator. A -> B (A implies B) Another way of stating the implies operator is with if…then: IF …

2023年8月10日 · The following is the truth table for implication $P \implies Q$. $$ \begin{array}{|c|c|c|} \hline P & Q & P \implies Q \\ \hline T&T&T \\ T&F&F \\ F&T&T \\ F&F&T \\ \hline \end{array} $$ For $P = T$, the truth values for implication makes intuitive sense. However, I, like many, don't intuitively understand the truth table for $P=F$.

2015年5月31日 · According to my textbook the implication P --> Q has the following truth table: I don't understand the last two rows. For example in the last row, how can we determine P --> Q if all we know is that both P and Q is false. Shouldn't the truth value be unknown in that case?

implication is {\it true}. This corresponds to the first line in the table. Suppose it's true that you get an A but it's false that I give you a dollar. Since I didn't keep my promise, the implication is false. This corresponds to the second line in the table. What if it's false that you get an A? Whether or not I give you a dollar, I haven't ...