All integers (negative, zero and positive) are divided into 2 sets, male and female; none of those sets is an empty set.
male number + female number = male number
male number * female number = female number
Given the above, for each of the following equations specify whether the result Ri is a female number, a male number, or could be either:
R1= female number * female number
R2= female number + female number
R3 = male number * male number
R4= male number + male number
Please justify your decisions.
What first comes to mind is female numbers are even (including zero) and male numbers are odd (including 1). These being the additive and multiplicative identities, they result in fitting the description.
But female numbers could also be multiples of any consistently chosen k, say 4. Male numbers would be those not divisible by 4.
Then two male numbers might add to either a male or a female number: 1 (male) + 1 (male) = 2 (male) but 2 (male) + 2 (male) = 4 (female). Two female numbers would add to another female number.
The same would apply to multiplication as one can see by using multiplication instead of addition in the examples shown in the paragraph above.
Posted by Charlie
on 2015-02-20 13:15:07