Question 1: Find out which of the following sentences are statements and which are not. Justify your answer.
(i) Listen to me, Ravi! (ii) Every set is a finite set.
(iii) Two non-empty sets have always a non-empty intersection.
(iv) The pussy cat is black. (v) Are all circles round?
(vi) Alt triangles have three sides. (vii) Every rhombus is a square.
(viii) has no real roots. (ix) This sentence is a statement.
(x) Is the earth round? (xi) Go!
(xii) The real number is less than 2. (xiii) There are 35 days in a month.
(xiv) Mathematics is difficult. (xv) All real numbers are complex numbers.
(xvi) The product of (-1) and 8 is 8.
Answer:
(i) Listen to me, Ravi!
The sentence “Listen to me, Ravi! “Is an exclamatory sentence. Therefore it is not a statement
(ii) Every set is a finite set.
This sentence is always false, because there are sets which are not finite. Therefore it is a statement.
(iii) Two non-empty sets have always a non-empty intersection.
This sentence is always false, because there are non-empty sets whose intersection is empty. Therefore it is a statement.
(iv) The pussy cat is black.
There are some cats which are black, and not black, So, the given sentence may or may not be true. Therefore it is not a statement.
(v) Are all circles round?
The given sentence is an interrogative sentence. Therefore it is not a statement.
(vi) All triangles have three sides.
The given sentence is a true declarative sentence. Therefore it is a statement.
(vii) Every rhombus is a square.
This sentence is always false, because Rhombuses are not a square. Therefore it is a statement.
(viii) has no real roots.
If you solve the equation, you will see there are no real roots. Therefore it is a statement.
(ix) This sentence is a statement.
The statement is not indicating the correct value, hence we can say that value contradicts the sense of the sentence. Therefore it is not a statement.
(x) Is the earth round?
The given sentence is an interrogative sentence. Therefore it is not a statement.
(xi) Go!
It is an exclamatory sentence. Therefore it is not a statement.
(xii) The real number is less than 2.
We cannot determine whether the sentence is true or false without knowing the value of x. Therefore it is not a statement.
(xiii) There are 35 days in a month.
It is a false assertive sentence. Therefore it is a false statement.
(xiv) Mathematics is difficult.
Mathematics could be difficult for some and easy for some people. So the sentence cannot be determined as a true or false sentence. Therefore it is not a statement.
(xv) All real numbers are complex numbers.
It is true as we can write a real number as x+i0. Therefore it is a true statement.
(xvi) The product of (-1) and 8 is 8.
The sentence is always false as (-1) times 8 is (-8). Therefore it is a false statement.
Question 2: Give three examples of sentences which are not statements. Give reasons for the answers.
Answer:
The three examples of sentences which are not statements are as follows:
i) May God bless you! – This sentence is an optive. So, we cannot assign a true or false to it and hence it is not a statement.
ii) Three plus four is six – The sentence is a false declarative sentence. Hence it is not a statement.
iii) Give me a glass of water – This sentence is an imperative sentence. It either expresses a request or a command. Hence it is not a statement.
(iv) How beautiful! – This is an exclamatory sentence. Hence not a statement.
(v) Open the door. – This is an order. Hence not a statement.
(vi) Where are you going? – This is an interrogative sentence. Hence not a statement.