Punjab State Board PSEB 11th Class Maths Book Solutions Chapter 14 Mathematical Reasoning Ex 14.4 Textbook Exercise Questions and Answers.
PSEB Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.4
Question 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) A 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.
Question 2.
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.
Answer.
(i) Contrapositive statement: If a number x is not odd, then xis not a prime number.
Converse statement: If x is odd, then it is a prime number.
(ii) Contrapositive statement: If two straight lines intersect in a plane than the lines are not parallel.
Converse statement: If two lines do not intersect in the sample plane, then the two lines are parallel.
(iii) Contrapositive statement : If the temperature of something is not low, then it is not cold.
Converse statement : If something has low temperature, then it is cold.
(iv) Contrapositive statement: If you know how to reason deductively, then you comprehend geometry.
(v) Converse statement: If you do not know how to reason deductively, then you can not comprehend geometry.
The given statement can be written as :
“If x is an even number, then x is divisible by 4”.
Contrapositive statement: If x is not divisible by 4, then x is not an even number.
Converse statement: If x is divisible by 4 then x is an even number.
Question 3.
Write each of the following statement 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 A+ in the class, it is necessary that you do the exercises of the book.
Answer.
(i) If you get a job, then your credential are good.
(ii) If the banana trees,stays warm for a month, then it will bloom.
(iii) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
(iv) If you get A+ in the class, then you do all exercises in the book.
Question 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.