Mathematical Reasoning (Ex – 14.1)
Question 1.
Which of the following sentences are statements? 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.
Solution:
(i) This sentence is false since the maximum number of days in a month can never exceed 31. Therefore, this sentence is a statement.
(ii) This sentence is subjective in the sense that for those who hate mathematics, it is difficult but for others it may not be. This means that this sentence is not always true. Hence it is not a statement.
(iii) This sentence is true as sum of 5 and 7 is greater than 10. Hence it is a statement.
(iv) This sentence is subjective in the sense that it depends on the number that is being squared. Hence it is not a statement.
(v) This sentence is sometimes true and sometimes false since sides in squares and rhombuses have equal length whereas rectangles and trapeziums have unequal length. Hence it is not a statement.
(vi) This sentence is an order and so, it is not a statement.
(vii) This sentence is false as product of (-1) and 8 is -8. So, it is a statement.
(viii) This sentence is true and therefore it is a statement.
(ix) It is not clear from the context which day is referred. Therefore, it is not a statement.
(x) All real numbers can be written in the form of complex numbers. So, this sentence is true and it is a statement.
Question 2.
Give three examples of sentences which are not statements. Give reasons for the answers.
Solution:
(i) Who are you?
This sentence is an interrogative sentence. Hence, it is not a statement.
(ii) May God bless you!
This sentence is an exclamatory sentence. Hence, it is not a statement.
(iii) How are you?
This sentence is an interrogative sentence. Hence, it is not a statement.
