Write the contrapositive and converse of the following statements.
(i) If x is a prime number, then x is odd.
(ii) If the two lines are parallel, then they do not intersect in the same plane.
(iii) Something is cold implies that it has low temperature.
(iv) You cannot comprehend geometry if you do not know how to reason deductively.
(v) x is an even number implies that x is divisible by 4.
Write the contrapositive and converse of the following statements.
(i) If x is a prime number, then x is odd.
(ii) If the two lines are parallel, then they do not intersect in the same plane.
(iii) Something is cold implies that it has low temperature.
(iv) You cannot comprehend geometry if you do not know how to reason deductively.
(v) x is an even number implies that x is divisible by 4.
(i) 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 of given statement is:
If x is not odd, then x is not a prime number. The converse of given statement is: If x is an odd number then x is a prime number.
(ii) Here p: Two lines are parallel.
q: They do not intersect in the same plane.
Now ~p: Two line are not parallel.
~q: They intersect in the same plane. The contrapositive of given statement is: If two lines intersect in the same plane, then they are not parallel.
The converse of the given statement is: If the two lines do not intersect in the same plane, then they are parallel.
(iii) Here p. Something is cold.
q: It has low temperature.
Now ~p: Something is not cold.
~q: It has not low temperature.
The contrapositive of given statement is: If something does not have low temperature then it is not cold. The converse of given statement is: If something has low temperature then it is cold.
(iv) Here p: You can not 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 of given statement is: If you can comprehend geometry, then you know how to reason deductively. The converse of given statement is: If you cannot comprehend geometry, then you do not know how to reason deductively.
(v) Here p: x is an even number.
q: xis divisible by 4.
Now ~p: x is not an even number.
~q: x is not divisible by 4.
The contrapositive of given statement is:
If x is not divisible by 4, then x is not an even number.
The converse of given statement is:
If x is divisible by 4, then x is an even number.
(i) 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 of given statement is:
If x is not odd, then x is not a prime number. The converse of given statement is: If x is an odd number then x is a prime number.
(ii) Here p: Two lines are parallel.
q: They do not intersect in the same plane.
Now ~p: Two line are not parallel.
~q: They intersect in the same plane. The contrapositive of given statement is: If two lines intersect in the same plane, then they are not parallel.
The converse of the given statement is: If the two lines do not intersect in the same plane, then they are parallel.
(iii) Here p. Something is cold.
q: It has low temperature.
Now ~p: Something is not cold.
~q: It has not low temperature.
The contrapositive of given statement is: If something does not have low temperature then it is not cold. The converse of given statement is: If something has low temperature then it is cold.
(iv) Here p: You can not 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 of given statement is: If you can comprehend geometry, then you know how to reason deductively. The converse of given statement is: If you cannot comprehend geometry, then you do not know how to reason deductively.
(v) Here p: x is an even number.
q: xis divisible by 4.
Now ~p: x is not an even number.
~q: x is not divisible by 4.
The contrapositive of given statement is:
If x is not divisible by 4, then x is not an even number.
The converse of given statement is:
If x is divisible by 4, then x is an even number.
