GSEB Class 11 Maths Solutions Chapter 14 Mathematical Reasoning Exercise 14.1

Question 1. Which of the following sentences are statements? Give reasons for your answer.
1. There are 35 days in a month.
2. Mathematics is difficult.
3. The sum of 5 and 7 is greater than 10.
4. The square of a number is an even number.
5. The sides of a quadrilateral have equal lengths.
6. Answer their questions.
7. The product of (- 1) and 8 is 8.
8. The sum of interior angles of a triangle is 180°.
9. Today is a windy day.
10. All real numbers are complex numbers.
Answer:
1. Statement: It is false to state that a month has 35 days.
2. Sentence: Mathematics might be challenging for some individuals, while it could be simple for others.
3. Statement: It is correct that when you add 5 and 7, the total is more than 10.
4. Sentence: The square of any number can either be an even or an odd number. For example, \( 2^2 = 4 \) (even), and \( 3^2 = 9 \) (odd).
5. Sentence: A quadrilateral's sides might have equal measurements, such as in a rhombus or a square, or the quadrilateral could possess unequal sides.
6. Sentence: This sentence represents an instruction or command.
7. Statement: This is incorrect because multiplying -1 by 8 does not yield 8.
8. Statement: It is correct that the total measure of a triangle's interior angles is 180°.
9. Sentence: This is not a definite statement because its truthfulness depends on the specific day, which is unclear.
10. Statement: It is correct that all real numbers can be represented as complex numbers in the format \( a + i.0 \).
In simple words: A sentence is a statement if it is clearly either true or false. We checked each sentence to see if we could definitely say it was true or false, and explained why.

Exam Tip: When identifying statements, ensure the sentence is either definitively true or definitively false, regardless of context or opinion. Commands or questions are never statements.

Question 2. Give three examples of sentences which are not statements. Give reasons for the answers?
Answer:
1. It is a rainy month. This is not a statement because the specific rainy month is undefined, making it impossible to determine its truth.
2. She is very beautiful. This is not a statement because 'she' is not identified, and 'beautiful' is subjective, so its truth cannot be verified.
3. You are a brave boy. This is not a statement as 'you' is not specified, and bravery is subjective, preventing verification of its truth.
In simple words: Sentences that ask questions, give orders, or express personal opinions are not statements because we cannot say for sure if they are true or false.

Exam Tip: Sentences that are subjective, questions, commands, or expressions of opinion are generally not considered mathematical statements because their truth value cannot be definitively established.