RBSE Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.1

Rajasthan Board RBSE Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.1 Textbook Exercise Questions and Answers.

RBSE Class 11 Maths Solutions Chapter 14 Mathematical Reasoning Ex 14.1

Question 1.
Which of the following sentences are statement? Give reasons for your answer.
(i) There are 35 days in a month.
(ii) Mathematics is difficult.
(iii) The sum of 5 and 7 is greater than 10.
(iv) The square of a number is an even number.
(v) The sides of a quadrilateral have equal length.
(vi) Answer this question.
(vii) The product of (-1) and 8 is 8.
(viii) The sum of all interior angles of a triangle is 180°.
(ix) Today is a windy day.
(x) All real numbers are complex numbers.
Answer:
(i) Given sentence is false, since no month contains 35 days. Thus, ft is a, statement but false.

(ii) “Mathematics.is difficult” This sentence shows uncertainity. Since, mathematics may be difficult for some and easy for others. Thus, it is true and false both. Thus, it is not a statement.'

(iii) “ The sum of 5 and 7 is greater than 10” This statement is true, since 5 + 7 = 12 which is more than 10. Thus, given sentence is a statement, since it is true.

(iv) “The square of a number is an even number”. Square of some numbers is an even number and square of some numbers is odd number.
For example : 2² = 4, 4² =16, 6² = 36, 8² =64 etc.
(square of even number) and 1² =1, 3² = 9, 5² = 25, 7² =49
(square of odd number)
Then, given sentence is true and false both.
Thus, it is not statement.

(v) “The sides of a quadrilateral have equal length”.
Above sentence is sometimes true and sometimes false as sides of square and rhombus are equal i.e. of same length and length of trapezium, rectangle parallelogram are not of equal length.
Thus, this sentence is sometimes true and sometimes false. Thus, it is not a statement.

(vi) “ Answer this question”
This sentence is order.
Thus, it is not a statement.

(vii) “The product of (-1) and 8 is 8”.
This sentence is false since product of -1 and 8 (-1 × 8) = -8.
Thus, it is statement.

(viii) Since, sum of all interior angles of a triangle is 18° C. Thus, it is a statement.
(ix) “Today is a windy day”.
This sentence shows uncertainity.
Thus, it is not a statement.

(x) “All real numbers are complex number”. Any real number can be represent in the form of complex number, as- If a is any real number then it can be written in the form a + io, which is always true. Thus, it is statement.

Question 2.
Give three examples of sentences which are not statements. Give reasons for the answers.
Answer:
The sentences which are true as well as false cannot be statements.
Example 1. Sum of x and y is greater than 2.
If x = 1 and y = 2.
then x + y = 1 +2 =3 which is more than 2 then. It is true for x = 1 and y = 2.
But, if x = 1, y - -1
x + y = 1 + (-1) = 1-1 = 0 which is less than 2.
Thus, it is false for x = 1, y - -1 Thus, it is not a statement.

Example 2. “Group of good students of any class”. We cannot say clearly, whether any student is good or not. Student x may be good according to some people and not good according to other people. Thus, it is not statement.

Example 3. “Value of sin θ remains always more than 0.” We know that, for any angle θ.
Value of sin θ may be positive and negative.
Thus, above sentence is true as well as false.
Thus, it is not statement.