Answer to Question #331361 in Discrete Mathematics for che

Question

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

1. It is necessary to do your homework to get the passing grade.

a.  Converse (q →p) =

b. Contra positive (q→¬p )=

c.  Inverse (p→¬q ) =  

  

2. You can access the school Wifi only if you are enrolled.

a.  Converse (q →p) =

b.  Contra positive (q→¬p )=

c.  Inverse (p→¬q ) =   

 

3.   Mark gets a high grade whenever he studies his lesson.

a. Converse (q →p) =

b. Contra positive (q→¬p )=

c. Inverse (p→¬q ) =

4.  If you read your lessons everyday, you will pass all your course.

a.  Converse (q →p) =

b.  Contra positive (q→¬p )=

c.  Inverse (p→¬q ) =

  

5.  If it rains today, I will stay home and read my lessons.

d. Converse (q →p) =

e. Contra positive (q→¬p )=

f. Inverse (p→¬q ) =

Answer 1

1. It is necessary to do your homework to get the passing grade.= If do your homework, then get the passing score

• a.  Converse (q →p) = If get passing score then do your homework
• b. Contra positive (q→¬p )= if get passing score then do not do your homework
• c.  Inverse (p→¬q ) =  if do your homework then do not get passing score

2. You can access the school Wifi only if you are enrolled. = If you enrolled then you can access school wifi

• a.  Converse (q →p) = if you can access school wifi then you enroll
• b. Contra positive (q→¬p )= If you can access school wifi then you do not enroll
• c.  Inverse (p→¬q ) =  If you enrolled then you can not access school wifi

3.   Mark gets a high grade whenever he studies his lesson. = If Mark studies his lesson then he gets a high grade

• a.  Converse (q →p) = if Mark gets a high grade then he studies his lesson
• b. Contra positive (q→¬p )= If Mark gets a high grade then he doesn't study his lesson.
• c.  Inverse (p→¬q ) =  if Mark studies his lesson then he doesn't get a high grade

4.  If you read your lessons everyday, you will pass all your course. = If you read your lessons everyday then you will pass all your course.

• a.  Converse (q →p) = If you will pass all your course then you read your lessons everyday
• b. Contra positive (q→¬p )= If you will pass all your course then you don't read your lessons everyday
• c.  Inverse (p→¬q ) =  If you read your lessons everyday then you will not pass all your course

5.  If it rains today, I will stay home and read my lessons. = If it rains today then I will stay home and read my lessons.

• a.  Converse (q →p) = If I will stay home and read my lessons then it rains.
• b. Contra positive (q→¬p )= If I will stay home and read my lessond then it doesn't rain.
• c.  Inverse (p→¬q ) =  If it rains then I will not stay home or don't read my lessons.