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
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
contrapositive is as follows.
If a number x
is not odd, then x
is not a prime number.
The converse is as
follows.
If a number x
is odd, then it is a prime number.
(ii) The
contrapositive is as follows.
If two lines
intersect in the same plane, then they are not parallel.
The converse is as
follows.
If two lines do not
intersect in the same plane, then they are parallel.
(iii) The
contrapositive is as follows.
If something does
not have low temperature, then it is not cold.
The converse is as
follows.
If something is at
low temperature, then it is cold.
(iv) The
contrapositive is as follows.
If you know how to
reason deductively, then you can comprehend geometry.
The converse is as
follows.
If
you do not know how to reason deductively, then you cannot comprehend
geometry.
(v) The given
statement can be written as follows.
If x
is an even number, then x
is divisible by 4.
The contrapositive
is as follows.
If x
is not divisible by 4, then x
is not an even number.
The converse is as
follows.
If x
is divisible by 4, then x
is an even number.
(i) The contrapositive is as follows.
If a number x is not odd, then x is not a prime number.
The converse is as follows.
If a number x is odd, then it is a prime number.
(ii) The contrapositive is as follows.
If two lines intersect in the same plane, then they are not parallel.
The converse is as follows.
If two lines do not intersect in the same plane, then they are parallel.
(iii) The contrapositive is as follows.
If something does not have low temperature, then it is not cold.
The converse is as follows.
If something is at low temperature, then it is cold.
(iv) The contrapositive is as follows.
If you know how to reason deductively, then you can comprehend geometry.
The converse is as follows.
If you do not know how to reason deductively, then you cannot comprehend geometry.
(v) The given statement can be written as follows.
If x is an even number, then x is divisible by 4.
The contrapositive is as follows.
If x is not divisible by 4, then x is not an even number.
The converse is as follows.
If x is divisible by 4, then x is an even number.
