In: Statistics and Probability
Is choosing an orange and a fruit from a basket mutually exclusive or inclusive?
Before answering this question we have to make sure that we correctly understand the biology of this problem.
Most of us would say that an orange is a fruit. However, technically, it's a special type of berries. Here is a quote from Wikipedia article Berry :
The fruit of citrus, such as the orange, kumquat and lemon, is a berry with a thick rind and a very juicy interior that is given the special name hesperidium .
If we accept this terminology, an orange is not a fruit and a fruit is not an orange. Therefore, we are dealing with mutually exclusive choice: either we choose an orange or a fruit.
But what if we are not that biologically savvy and consider an orange to be just another fruit?
In this case, choosing an orange implies choosing a fruit. So, these choices are not mutually exclusive.
At the same time, choosing a fruit might not necessarily imply choosing an orange, if there are other fruits in the basket, like plums. So, we have inclusivity only in one direction, from orange to fruit, but not the other way around.
Therefore, there is no mutual inclusivity either.
There is no mutual inclusivity either.