Problem 1: Give the converse and contrapositive of the following propostions: If
ID: 3881729 • Letter: P
Question
Problem 1:
Give the converse and contrapositive of the following propostions:
If the traffic light is red, then cars must stop.
If the fruit is red, then it is an apple.
Unrest is sufficient for change.
A right implies a responsibiility.
The right to search for the truth implies also a duty.
Speak only if it improves upon the silence.
Problem 2: State whether the following is true of false.
If it is nighttime, then it is 3:00 A.M.
If it is 3:00 A.M., then it is nighttime.
It is 3:00 A.M. if and only if it is nighttime
Explanation / Answer
For the proposition P-> Q , the proposition Q->P is called its converse, and the proposition Q'->P' is called its contrapositive.
Problem 1:
a) If the traffic light is red, then cars must stop.
Converse: If cars must stop, then the traffic light is red.
Contrapositive: If cars must not stop, then the traffic light is not red.
b) If the fruit is red, then it is an apple.
Converse: If it is an apple, then the fruit is red.
Contrapositive: If it is not an apple, then the fruit is not red.
c) Unrest is sufficient for change.
First we will convert the sentence in if-then then we will write converse and contrapositive.
If there is unrest, then there is change.
Converse: If there is change, then there is unrest.
Contrapositive: If there is no change, then there is no unrest.
d) A right implies a responsibiility.
If there is a right then there is responsibility.
Converse: If there is responsibility, then there is a right.
Contrapositive: If there is no reponsibility, then there is no right.
e) The right to search for the truth implies also a duty.
If there is right to search for the truth, then there is a duty.
Converse: If there is a duty, then there is right to search for the truth.
Contrapositive: If there is no duty, then there is no right to search for the truth.
f) Speak only if it improves upon the silence.
Converse: If it improves upon the silence, then speak.
Contrapositive: If it does not improve upon the silence, then don't speak.
Problem 2:
a) If it is nighttime, then it is 3:00 A.M. - False
b) If it is 3:00 A.M., then it is nighttime. -True
c) It is 3:00 A.M. if and only if it is nighttime -False