Which of the following sentences are statements? In case of a statement mention whether it is true or false.
(i) The sun is a star.
(ii) $\sqrt{7}$ is an irrational number.
(iii) The sum of 5 and 6 is less than 10 .
(iv) Go to your class.
(v) Ice is always cold.
(vi) Have you ever seen the Red Fort?
(vii) Every relation is a function.
(viii) The sum of any two sides of a triangle is always greater than the third side.
(ix) May God bless you!
(i) The sun is a star is a statement. It is a scientifically proven fact that the sun is a star and, therefore this sentence is always true. Hence it is a statement, and it is true
Note: A sentence is called a mathematically acceptable statement if it is either true or false but not both.
(ii) $\sqrt{7}$ is an irrational number. An irrational number is any number which cannot be expressed as a fraction of two integers. $\sqrt{7}$ cannot be expressed as a fraction of two integers, so $\sqrt{7}$ is an irrational number; therefore the sentence is always true. Hence it is a statement, and it is true.
Note: A sentence is called a mathematically acceptable statement if it is either true or false but not both.
(iii) The sentence is true because the sum of 5 and 6 is not less than 10 . Sum of 5 and 6 is 11 , which is not less than 10 . Hence it is a statement. The statement is true.
Note: A sentence is called a mathematically acceptable statement if it is either true or false but not both.
(iv) This sentence 'Go to your class' is an order. Hence it is not a statement.
Note: A sentence which is in the form of an order, exclamation and question is not a statement.
(v) Ice is always cold is a statement. It is scientifically proven the fact that ice is always cold and, therefore the sentence is always true.
Hence it is a statement, and it is true.
Note: A sentence is called a mathematically acceptable statement if it is either true or false but not both.
(vi) The sentence 'Have you ever seen the Red Fort? Is a question, hence it is not a statement.
Note: A sentence which is in the form of an order, exclamation and question is not a statement.
(vii) The sentence 'Every relation is a function' is a statement. There are relations which are not functions. Therefore the sentence is false. Hence it is a statement, and it is false.
Note: A sentence is called a mathematically acceptable statement if it is either true or false but not both.
(viii) The sentence 'The sum of any two sides of a triangle is always greater than the third side' is a statement. Because the sum of any two sides of the triangle is always greater than the third side. Hence the statement is true.
(ix) The sentence 'May God bless you!' is an exclamation. Hence it is not a statement.
Note: A sentence which is in the form of an order, exclamation and question is not a statement.