question_answer 6)

State whether the following statements are true or false. (a) The sum of three odd numbers is even. (b) The sum of two odd numbers and one even number is even. (c) The product of three odd numbers is odd. (d) If an even number is divided by 2, the quotient is always odd. (e) All prime numbers are odd. (f) Prime numbers do not have any factor. (g) Sum of two prime numbers is always even. (h) 2 is the only even prime number. (i) All even numbers are composite numbers. (j) The product of two even numbers is always even.

Answer:

                (a) False, because the sum of three odd numbers is always odd. e.g.        3 + 5 + 7 = 15 and 9 + 11 + 13 = 33              (odd) (b) True, because the sum of two odd numbers and one ever number is always an even number. e.g.        \[\begin{matrix}    3  \\    \downarrow   \\    \text{Odd}  \\ \end{matrix}+\begin{matrix}    7  \\    \downarrow   \\    \text{Odd}  \\ \end{matrix}+\begin{matrix}    6  \\    \downarrow   \\    \text{Even}  \\ \end{matrix}=16\]           (even) (c) True, because product of three odd numbers is always odd. e.g. 3 x 5 x 7 = 105 (odd) (d) False, because if an even number is divided by 2, the quotient is always an even number. e.g.        \[\frac{24}{2}=12\]          (even) (e) False, because 2 is only even prime number. So, all prime numbers are not odd. (f) False, because prime numbers have two factors, which are 1 and number itself. e.g. 5 is a prime number and has two factors 1 and 5. (g) False, because sum of two prime numbers is either odd or even. e.g.        2 + 3 = 5 (odd) and 3 + 7 = 10 (even) (h) True, (i) False, because all even numbers are not composite numbers. e.g. 2 has the factors 1 and 2 only, so it is a prime number but not a composite number. (j) True, the product of two even numbers is always even. e.g. 2 x 4 = 8 (even)