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Earn +20 ptsQ: Is set of integers is a group under multiplication?
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Is the set of even integers closed under multiplication?
Yes
Is the set of all negative integers a group under addition?
no
Why is a set of positive integers not a group under the operation of addition?
The set of positive integers does not contain the additive inverses of all but the identity. It is, therefore, not a group.
Which set is closed under the operation multiplication?
Any set where the result of the multiplication of any two members of the set is also a member of the set. Well known examples are: the natural numbers (ℕ), the integers (ℤ), the rational numbers (ℚ), the real numbers (ℝ) and the complex numbers (ℂ) - all closed under multiplication.
Is the set of all even integers closed with respect to multiplication?
Yes, it is.
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