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3 November, 05:27

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.

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Answers (1)
  1. 3 November, 05:49
    0
    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.
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