Question

Simplify p∨(q∧¬q) to p 1. select a law from the right to apply p∨(q∧¬q)

Answer 1

To simplify p∨(q∧¬q) to p, apply the law of the excluded middle. q∧¬q evaluates to false because q and ¬q cannot both be true. Therefore, the expression simplifies to p.

Step-by-step explanation:

To simplify the expression p∨(q∧¬q) to p, we can apply the law of the excluded middle. This logical law states that for any statement, either that statement or its negation is true. In this case, q∧¬q evaluates to false because it is not possible for both q and ¬q to be true at the same time. Therefore, the expression simplifies to p∨false, which is equivalent to p.