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The set of numbers, S, has the following two properties: the product o
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09 Nov 2021, 07:03
09 Nov 2021, 07:03
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Question Stats:
69% (01:09) correct
30% (01:23) wrong based on 23 sessions
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The set of numbers, S, has the following two properties: the product of any two numbers in set S is also an element of set S, the sum of any two numbers in set S is also an element of set S. Which of the following could be set S?
Indicate all that apply.
S = {all even integers}
S = {all odd integers}
S = {all real numbers}
S = {all positive real numbers}
S = {all negative real numbers}
Indicate all that apply.
S = {all even integers}
S = {all odd integers}
S = {all real numbers}
S = {all positive real numbers}
S = {all negative real numbers}
Re: The set of numbers, S, has the following two properties: the product o
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01 Dec 2021, 03:23
01 Dec 2021, 03:23
Expert Reply
OE
(A) is correct because the sum of two even integers is even, and the product of two even integers is even. For example, 2 + 4 = 6, 10 + –8 = 2, 12 × 4 = 48. (B) is not correct because the sum of two odd integers is not odd. For example, 1 + 3 = 4. (C) is correct: the Real number system is closed under addition and multiplication, meaning that any two real numbers when added or multiplied will produce another real number. (D) is correct, because when positive numbers are added or multiplied, the result is positive. (E) is not correct, because the product of two negative real numbers is not negative but positive. Answer is (A), (C), and (D).
(A) is correct because the sum of two even integers is even, and the product of two even integers is even. For example, 2 + 4 = 6, 10 + –8 = 2, 12 × 4 = 48. (B) is not correct because the sum of two odd integers is not odd. For example, 1 + 3 = 4. (C) is correct: the Real number system is closed under addition and multiplication, meaning that any two real numbers when added or multiplied will produce another real number. (D) is correct, because when positive numbers are added or multiplied, the result is positive. (E) is not correct, because the product of two negative real numbers is not negative but positive. Answer is (A), (C), and (D).
gmatclubot
Re: The set of numbers, S, has the following two properties: the product o [#permalink]
01 Dec 2021, 03:23
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