Question

Check all the statements that are true:

Answer 1

Answer:

The true statements are;

A, B, G, H, I, J

Step-by-step explanation:

To answer the question, we test each option as follows

A. If a and b both divide c, then ab divides c².

The above statement is true as c/a exists,

c/b exits therefore c²/ab = c/a×c/b

B. If p and q are distinct primes, then p2q2 has exactly 11 positive divisors.

The above statement is true as p² and q² each have 3 positive divisors, therefore, p²q² will also have pq and p²q² as possible divisors, therefore, true

C. If p and q are distinct primes, then p+q is prime as well.

The above statement is not correct as 5 + 7 = 12 an even number

D. If a divides b and c divides d, then a+c divides b+d.

The above statement is not correct as

8 is divisible by 2 and

9 is divisible by 3

but 17 is not divisible by 5

E. If p is prime, then so is p+2.

The above statement is not correct as 7 + 2 = 9 which is divisible by 3

G. If a and b both divide c, and a and b are relatively prime, then ab divides c.

The above statement is true as both a and b are factors of c

H. There are infinitely many prime numbers.

The above statement is true as there are infinitely many numbers

I. If p is prime, then p2 has exactly 3 positive divisors.

The above statement is true

1, p and p²

J. There are three consecutive odd numbers that are prime.

The above statement is true

3, 5, 7.