Question

For any whole numbers a,b,c is true that (a+b)+c = a+(c+b)? give reason​

Answer 1

Answer:

answer for the given problem is given

Answer 2

Answer:

We are to prove that (a + b) + c = a + (b + c) for all a, b, c belonging to N. We first check the case c = 1 for all a, b. Three applications of definition (given above) give

(a + b) + 1 = (a + b)' = a + b ' = a + (b + 1).

Next, assume the associative law true for a particular value of c and for all a, b. Then we verify it for c' as follows:

(a + b) + c' = (a + b) + (c + 1) (definition)

(a+b)+c′=(a+b)+(c+1) (definition)

=((a+b)+n)+1 (case c=1) ?

We consider (a+b) as a single number; call it A.

We have:

A+(c+1)=(A+c)+1

and it holds by the base case (k=1) already proved.

so,

= ((a + b) + c) + 1 (case c = 1)

= (a + (b + c)) + 1 (induction hypothesis)

= a + ((b + c) + 1) (case c = 1)

= a + (b + (c + 1)) (case c = 1)

= a + (b + c') (definition). proved