Answer to Question #312419 in Discrete Mathematics for Donnel

Question

D. Write in the form " if p then q", then write converse, inverse and contra positive of each of the following implications.

1. it is necessary to do your homework to get a passing grade.
2. if you read your lesson everyday, you will pass all your courses.

Answer 1

Solution (1)

 

Let    p = doing homework

 

           q = getting passing grade

 

If p then q

If you do your homework, then you get a passing grade

 

Convers

If you want to get a passing grade, then you have to do your homework

 

Inverse

If you do not do your homework, then you will not get a passing grade.

 

Contrapositive

If you don’t want to get a passing grade, then you don’t have to do your homework.

 

 

 

 

Solution (2)

 

Let    p = you read your lesson every day

 

           q = pass all the courses

 

If p then q

If you read your lesson every day, then you will pass all your courses

 

Convers

If you want to pass all your courses, you need to read your lessons every day

 

Inverse

If you don’t read your lessons every day, then you won’t pass all your courses.

 

Contrapositive

If you don’t want to pass all the courses, then you don’t need to read your lessons every day.