Actually Venn diagrams can be very useful in exploring combinations you haven’t considered before.

To use an example: Pokemon!

Say you have fire, psychic and flying types, and you are making new pokemon for a new game. You might want to make some new combinations that haven’t existed before. You take all the pokemon, put them in a Venn diagram with these 3 categories of types: Moltres is flying and fire, easy. But are there Psychic Flying pokemon? (turns out yes – Xatu) Or Psychic Fire pokemon? (turns out yes, Delphox)

In this way you can find options for combinations you haven’t had before. (And I’m pretty sure this happens regularly in Pokemon every time they add a new category of type).

This would make all Euler diagrams redundant.

You could correct this example by changing ‘mammals’ to ‘creatures with antlers’. Then if in the future someone were to breed a bird with antlers, it would then make the Euler diagram incorrect.

Your second example lacks clarity. I assume your ‘red card’ and ‘black card’ classifications mean the colour of the suit symbol on the card (note that J, Q and K cards often contain many colours).

I wondered about creating a new suit with a mixture of red and black. If your classification means the colour of any part of the suit symbol then your example is correct.

However, if ‘red card’ means an all-red suit symbol then such a card could not go in the intersection because it cannot go in the ‘red’ set or in the ‘black’ set as it is neither. A card cannot be all-red and all-black at the same time.

An earlier comment said that a Venn diagram was useless because it contains info that does not exist in the real world. I think this view was formed from inspection of your examples. A Venn diagram that shows “all possible logical relationships that could ever exist” does contain valuable information.

(1)Let U be the students in the class today. define a subset A of U based on some quality or characteristic. (something other than gender). clearly define A in words. You do not need to place people in set A by name. let F= females and M= males.

 solve:
 A=?,
 A’=?,  
AnF=?
F’=?, 
MUF=?, 
MnF=?,
 n(U)=?, 
n(F)=?, 
n(M)=?.I need tour help with these question:

(2) Make up a real world example where ACBCU. define A, B, and U and draw an euler diagram.