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