Consider each set of numbers and determine if the set has an additive identity, additive inverse, multiplicative identity, or a multiplicative inverse. Explain your reasoning for each. a. the set of natural numbers.

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The set of natural numbers is&amp;nbsp;{1,2,3,4,…}.The additive identity of a number, aa, is always 0 since&amp;nbsp;a+0=0+a=a. The set of all natural numbers lacks an additive identity because 0 is not a part of it.The additive inverse of a number aa is −a since&amp;nbsp;a+(−a)=−a+a=0. The set of natural numbers does not include any negative numbers so for all natural numbers a, the additive inverse of −a would not be a natural number. In that case, the set lacks an additive inverse.The multiplicative identity of a number aa is always 1 since&amp;nbsp;a⋅1=1⋅a=a. Since 1 is included in the set of the natural numbers, then the set does have a multiplicative identity does have a multiplicative identity.The multiplicative inverse of a number aa is always&amp;nbsp;1a&amp;nbsp;since&amp;nbsp;a⋅1a=1. If aa is a natural number not equal to 1, then&amp;nbsp;1a&amp;nbsp;is not a natural number. For example,&amp;nbsp;a=2&amp;nbsp;would have a multiplicative inverse of&amp;nbsp;1a=12&amp;nbsp;which is not a natural number. The set of natural numbers then does not have a multiplicative inverse. ​

Consider each set of numbers and determine if the set has an additive identity, additive inverse, multiplicative identity, or a multiplicative inverse. Explain your reasoning for each. a. the set of natural numbers.

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