3) Define the following mathematical operations as relations. Are the relations

Question

3) Define the following mathematical operations as relations. Are the relations defined partial functions, total functions, or neither? a) The relation (a + b) =C, where a, b, and care natural numbers (it will be the form (a,bJRC) b) The cubic function b = a on the set of integers. c) The set of all alb such that a = b/2. d) The set of all pairs (a, b) such that a and b are distinct natural numbers and the two share no common divisor other than the other . (either a or b must cleanly divide into the other, and there is no other divisor shared between them). What condition must either a or b hold?

Explanation / Answer

a) It is a total function. becuase this relation holds for every set
   of natural numbers

b) It is partial becuase not every number is equal to the cube of a number

c) a,b share no common divisor other than other. Once either a or b gets
divided by other then there is no common divisor.This is a partial function
because it will not hold good for all the set of numbers.One condition can be
a and b will be prime. The other condition will be that if they are not prime
then if one of them is even then the other must be odd.However both can be odd.

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