So, the negation can be written as follows: The negation can be written in the form of a conjunction by using the logical equivalency \(\urcorner (P \to Q) \equiv P \wedge \urcorner Q\). Its negation is not a conditional statement. This conditional statement is false since its hypothesis is true and its conclusion is false. You do not clean your room and you can watch TV.įor another example, consider the following conditional statement: So the negation of this can be written as The idea is that if \(P \to Q\) is false, then its negation must be true. Is false? To answer this, we can use the logical equivalency \(\urcorner (P \to Q) \equiv P \wedge \urcorner Q\). If you do not clean your room, then you cannot watch TV, So what does it mean to say that the conditional statement The negation of a conditional statement can be written in the form of a conjunction. The logical equivalency \(\urcorner (P \to Q) \equiv P \wedge \urcorner Q\) is interesting because it shows us that the negation of a conditional statement is not another conditional statement. Since many mathematical statements are written in the form of conditional statements, logical equivalencies related to conditional statements are quite important. However, we will restrict ourselves to what are considered to be some of the most important ones. It is possible to develop and state several different logical equivalencies at this time. \(\urcorner (P \vee Q) \equiv \urcorner P \wedge \urcorner Q\) Table 2.3: Truth Table for One of De Morgan’s Laws \(P\) Table 2.3 establishes the second equivalency.
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