Question

In: Advanced Math

Using the successor function prove distribution over addition. Do this in a detailed proof.

Expert Solution

Property :

which is called disrtibutive rule for multiplication over addition.

Proof : We will prove this property by using the principle of mathematical induction. Let X be a set of all such that

Then Assume that We must show that

As before we use a chain of equalities.

by the definition. Since Thus If we now apply the associative law for addition we have Inside the first set of braces we apply the commutative rule for addition and have by the associative law of addition applied inside the parentheses. We now apply the commutative law of addition within the paranthesesand the associative law of addition to find By definition the last expression is Thus and the distributive law is proved.

Colby Messinger answered 2 years ago

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Question

Using the successor function prove distribution over addition. Do this in a detailed proof.

Solutions

Expert Solution

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