** ****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 180 ^{0} in a triangle.**

**(i) Yesterday was a cloudy day. **

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

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**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 180^{0}. **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.**

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**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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