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.
