NCERT Class XI Mathematics - Mathematical Reasoning - Solutions
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Question : 11
Total: 25
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) 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.
Solution:
(i) The contrapositive of given statement is:
If a number 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) The contrapositive of given statement is:
If two lines intersect in the same plane, then they are not parallel.
The converse of given statement is:
If two lines do not intersect in the same plane, then they are parallel.
(iii) The contrapositive of given statement is:
If something is not at low temperature, then it is not cold.
The converse of given statement is:
If something is at low temperature, then it is cold.
(iv) The contrapositive of given statement is:
If you know how to reason deductively, then you can comprehend geometry.
The converse of given statement is:
If you do not know how to reason deductively, then you cannot comprehend geometry.
(v) 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.
If a number 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) The contrapositive of given statement is:
If two lines intersect in the same plane, then they are not parallel.
The converse of given statement is:
If two lines do not intersect in the same plane, then they are parallel.
(iii) The contrapositive of given statement is:
If something is not at low temperature, then it is not cold.
The converse of given statement is:
If something is at low temperature, then it is cold.
(iv) The contrapositive of given statement is:
If you know how to reason deductively, then you can comprehend geometry.
The converse of given statement is:
If you do not know how to reason deductively, then you cannot comprehend geometry.
(v) 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.
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