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)
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