Question

Numbers p and q are positive integers.

Which statements are always true?

Choose all answers that are correct.

A.
p + q is a positive integer

B.
p – q is a negative integer

C.
p • q is a positive integer

D.
is a positive integer

Answer 1

True—>A. p + q is a negative integer. When you add a negative, its the same as subtraction, and when you subtract from a negative, the number gets smaller.
True—>B. p x q is a positive number. When you multiply two negatives, the answer is always a positive.
False—>C. -1 - (-2) is the same as -1 + 2, which is positive.
False—>D. The rules for multiplication apply to division also.

Answer 2

Is the set of multiples of 5 closed under division? Explain why or provide a counterexample if not.

A.
Yes, because the quotient of any two multiples of 5 is also a multiple of 5.

B.
Yes, because the quotient of any two multiples of 5 is also a multiple of 10.

C.
No, and a counterexample is 100 ÷ 5 = 20.

D.
No, and a counterexample is 25 ÷ 50 = .

Answer 3

New Q please! :)