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Which of the following statements are true? (i) Sum of two prime numbers is always a prime number. (ii) A composite number can be odd. (iii) '2' is the only even prime number. (iv) '1' is the smallest prime number.

Which of the following statements are true? (i) Sum of two prime numbers is always a prime number. (ii) A composite number can be odd. (iii) '2' is the only even prime number. (iv) '1' is the smallest prime number. Correct Answer (ii) and (iii)

Explanation:

Case (i): Sum of two prime numbers is always a prime number.

Suppose the two prime numbers are 5 and 7

⇒ 5 + 7 = 12, which is not a prime number

Thus, case (i) is false. 

Case (ii): A composite number can be odd.

Some composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, ....

So, the composite number can be both even or odd.

Thus, case (ii) is true. 

Case (iii): '2' is the only even prime number.

After 2, all the prime numbers are odd.

Thus, case (iii) is true.

Case (iv): '1' is the smallest prime number.

A prime number is a number that has two factors, 1 and itself.

But, 1 does not have two factors. 

∴ 1 is not a prime number.

Thus, case (iv) is false.

Hence, (ii) and (iii) are true. 

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