Numbers p and q are positive integers.
Which statements are always true?
Choose all answers that are correct.
p + q is a positive integer
p – q is a negative integer
p • q is a positive integer
is a positive integer
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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.
Is the set of multiples of 5 closed under division? Explain why or provide a counterexample if not.
Yes, because the quotient of any two multiples of 5 is also a multiple of 5.
Yes, because the quotient of any two multiples of 5 is also a multiple of 10.
No, and a counterexample is 100 ÷ 5 = 20.
No, and a counterexample is 25 ÷ 50 = .