1. Here p: x is a prime number.
q: x is odd.
Now, ~ p: x is not a prime number.
~ q: x is not odd.
The contrapositive statement is:
If x is not odd x is not a prime number.
The converse statement is:
If x is an odd, then x is a prime number.
2. Here p: Two lines are parallel.
q: They do not intersect in the same plane.
Now, ~ p: Two lines are not parallel.
~ q: They intersect in the same plane.
The contrapositive statement is:
If two intersect in the same plane then they are not parallel.
The converse statement is:
If the two lines do not intersect in the same plane, then they are parallel.
3. Here p: Something is cold.
q: It has low temperature.
Now, ~ p: Something is not cold.
~ q: It does not have low temperature.
The contrapositive statement is:
If something does not have low temperature then it is not cold.
The converse statement is:
If something has low temperature then it is cold.
4. Here p: You cannot comprehend geometry.
q: You do not know how to reason deductively.
Now, ~ p: You can comprehend geometry.
~ q: You know how to reason deductively.
The contrapositive statement is:
If you know how to reason deductively,
then you can comprehend geometry.
The converse statement is:
If you do not know how to reason deductively then you cannot comprehend geometry.
5. Here p: x is an even number.
q: x is divisible by 4.
Now, ~ p: x is not an even number.
~ q: x is not divisible by 4.
The contrapositive statement is:
If x is not divisible by 4 then x is not an even number.
The converse statement is:
If x is divisible by 4 then x is an even number.
