NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Exercise 14.4
Chapter 14 Mathematical Reasoning Exercise 14.4 Class 11 Maths NCERT Solutions is given here that are accurate so you can check your answers with these and boost your marks in the examinations. Practicing NCERT Solutions for Class 11 Maths will give you details how to apply important fomula and knowing the basic points of the chapter.
1. Rewrite the following statement with “if-then” in five different ways conveying the same meaning.
1. Rewrite the following statement with “if-then” in five different ways conveying the same meaning.
‘If a natural number is odd, then its square is also odd.’
Answer
(i) A natural number is odd implies that its square is odd.
(ii) The natural number is odd only if its square is odd.
(iii) If the square of a natural number is not odd then the natural number is also not odd.
(iv) For a natural number to be odd it is necessary that its square is odd.
(v) For a square of a natural number to be odd, it is sufficient that the number is odd.
2. 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.
Answer
(i) Given statement: If x is a prime number, then x is odd.
The contrapositive statement: If a number x is not odd, then x is not a prime number.
The converse statement: If a number x is odd, then it is a prime number.
(ii) Given statement: If the two lines are parallel, then they do not intersect in the same plane.
The contrapositive statement: If two lines intersect in the same plane, then they are not parallel.
The converse statement: If two lines do not intersect in the same plane, then they are parallel.
(iii) Given statement: Something is cold implies that it has low temperature.
The contrapositive statement: If something is not at low temperature, then it is not cold.
The converse statement: If something is at low temperature, then it is cold.
(iv) Given statement: You cannot comprehend geometry if you do not know how to reason deductively.
The contrapositive statement: If you know how to reason deductively, then you cannot comprehend geometry.
The converse statement: If you do not know how to reason deductively, then you cannot comprehend geometry.
(v) Given statement: x is an even number implies that x is divisible by 4.
It can be written as: “If x is an even number, then x is divisible by 4”.
The contrapositive statement: If x is not divisible by 4, then x is not an even number.
The converse statement: If x is divisble by 4, then x is an even number.
3. Write each of the following statements in the form ‘if-then’.
(i) “You get a job implies that your credentials are good”.
(ii) The Banana trees will bloom if it stays warm for a month.
(iii) A quadrilateral is a parallelogram if its diagonals bisect each other.
(iv) To get an A+ in the class, it is necessary that you do all the exercise of the book.
Answer
(i) If you get a job then your credentials are good.
(ii) If it stays warm for a month the Banana trees will bloom.
(iii) If diagonals of a quadrilateral bisect each other then it is a parallelogram.
(iv) If you get an A+ in the class then you do all the exercises of the book.
4. Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other.
(a) If you live in Delhi, then you have winter clothes.
(i) If you do not have winter clothes, then you do not live in Delhi.
(ii) If you have winter clothes, then you live in Delhi
(b) If a quadrilateral is a parallelogram, then its diagonals bisect each other.
(i) If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram.
(ii) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Answer
(a) (i) Contrapositive statement.
(ii) Converse statement.
(b) (i) Contrapositive statement.
(ii) Converse statement.