That is correct.
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If you mean the product, that's by definition. A composite number has smaller factors. If you multiply two positive integers, none of which is 1, together, then it follows that the product has smaller factors - namely, the numbers you multiplied together.
The sum of any two prime numbers is not always a composite number. The sum of 2 and 11 is 13, and 13 is a prime number, not a composite number.
Not necessarily.
Not always as for example 20+9 = 29 which is a prime number
No. If you multiply any numbers, those numbers are factors of whatever product you get. Therefore, this product is a composite number; it has atleast the two factors you multiplyed before. Compposite numbers are never prime. If the two factors above were prime, you would still end up with a composite number. For example: 3 times 5 equals 15. The factors of 15 are 1, 3, 5, and 15. 15 is composite. 7 time 51 equals 357. The factors of 357 are 1, 7, 51, and 357. 357 is composite.