Class 11 Maths Ncert Solutions Chapter 14 Ex 14.1 Mathematical Reasoning PDF

Class 11 Maths Ncert Solutions Ex 14.1

Class 11 Maths Ncert Solutions Chapter 14 Ex 14.1

 Q.1: State whether the following sentences are statements or not, and justify your answers.

(a) A month has 35 days.

(b) Mathematics is very tough

(c) Addition of two numbers such as 5 & 7 is larger than 10.

(d) The resultant of a square of a number is always an even number.

(e) The arms of a quadrilateral are having equal length.

(f) Answer the following questions.

(g) The multiplication result of two numbers such as 8 and (-1) is 8

(h) The interior angles summed up together results in 1800 in a triangle.

(i) Yesterday was a cloudy day.

(j) The numbers which are real are always complex numbers.

 

Sol:

(a) The maximum number of days in a month is 31.Hence, the statement is incorrect. Therefore, this isn’t a proved statement.

(b) Mathematics can be tough for someone and it can be easy for someone too. Hence it is a direct violation to the above question. Hence, this isn’t a statement.

(c) The sum of two numbers such as 5 and 7 is 12 which is larger than 10. Hence, the above-mentioned sentence is true. Therefore, this is a proved statement.

(d) Square of all numbers does not give even number as a result. Such as the square of a even number that is 4 is 16 which is a even number, but the square of a odd number such as 9 is 81 which is a odd number. Hence, the above mentioned statement is not fully true. Therefore, this isn’t a proved statement.

(e) The above sentence is true only in certain cases. In case of square, all the sides are having equal length whereas in case of a rectangle all the sides are not equal except the opposite sides are equal in length. Hence, above the statement is not true. Therefore, this isn’t a proved statement.

(f) Above mentioned sentence is a direct order given to someone in order to answer the upcoming questions. Therefore, this isn’t a proved statement.

(g) The multiplication of 8 and -1 is (–8). Therefore, the above mentioned sentence is incorrect. Hence, this is a proved statement.

(h) This sentence is correct because the addition of all interior angles of a triangle is 1800. Hence, this is a proved statement.

(i) The day which is being referred to in the above mentioned sentence is not at all clear. Therefore, this isn’t a proved statement.

(j) All real numbers can be written in a format such as (1) + 0(i) Therefore, the given sentence is always correct. Hence, this is a proved statement.

 

 

Q.2: Give 3 examples of each sentence which are not statements. Give justified reasons for the answers.

 

Sol:

The three examples of sentences, which are not statements, are as follows.

(i) Today is a cloudy day.

The day which is being referred to in the above mentioned sentence is not at all clear. Therefore, it is not a statement.

 

(ii) Mathematics is very tough

Mathematics can be tough for someone and it can be easy for someone too. Hence it is a direct violation to the above question. Therefore, it is not a statement.

 

(iii) Where are you going?

The above sentence is a question which contains ‘ you ‘ , and it is not at all clear from the above question who is being referred to . Therefore, it is not a statement.

 

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