Check all the statements that are true:

A. If a and b both divide c, then ab divides c2.
B. If p and q are distinct primes, then p2q2 has exactly 11 positive divisors.
C. If p and q are distinct primes, then p+q is prime as well.
D. If a divides b and c divides d, then a+c divides b+d.
E. If p is prime, then so is p+2.
F. If a and b both divide c, then ab divides c.
G. If a and b both divide c, and a and b are relatively prime, then ab divides c.
H. There are infinitely many prime numbers.
I. If p is prime, then p2 has exactly 3 positive divisors.
J. There are three consecutive odd numbers that are prime.

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.

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!