All batangos are crentons , some franters are volns, and some kijuxes are not batangos. If no kijuxes are franters, which of the following CANNOT be true, given each group was observed to have no more than 2 members.
a) All volns are crentons, as are all franters
b) those kijuxes that are volns are not crentons
c)all kijuxes are volns and some are batangos
d) some batangos are franters and some are kijuxes
I have a word solution, and I can post that if requested, but I was wondering if there was a way to construct venn diagrams that encapsulate the information and are easy to read off.
The challenge is to solve this in 1 min and 30 secs so I imagine a venn diagram would be much faster than trying to run through each of the cases. So the challenge is to not only find a solution, but find the fastest way to solve this.
First of all to make things easier, assign a simpler title to each category.
Consider batangos to be $A$.
Consider crentons to be $B$.
Consider franters to be $C$.
Consider volns to be $D$.
Consider kijuxes to be $E$.
You can rewrite the logic statements with the new names to get:
All $A$ are $B$.
Some $C$ are $D$.
Some $E$ are not $A$.
No $E$ are $C$.
This allows for an easier digestion of the important information in the question. The logic to proceed from here has been wonderfully covered in a comment by @joriki.