I am taking a discrete mathematics course and one of the questions asks to develop an English translation of a proposition.
The proposition has the following structure [Question 9 part H is where I am having issues]:
Here is an image of the question.
I posted the question on the course's Piazza page and a student answered this:
¬p∧(p∨¬q) {My original proposition}
≡
(¬p∧p)∨(¬p∧¬q)
Then saying:
(¬p∧p)∨(¬p∧¬q)
=
(p∨¬q) {The proposition that the student claims is == my original proposition.}
Obviously (p∨¬q) would be simpler to put in words than ¬p∧(p∨¬q). Finding an English statement for ¬p∧(p∨¬q) would be difficult as compared to (p∨¬q).
Is this true? And if so, why?