We have the following premises and associated Venn Diagrams:
"All dogs are mammals."
"All cats are mammals."
Combining the Venn
Diagrams for premises 1 and 2, we get the combined Venn Diagram.
However, if the deduction "all cats are dogs" is valid, then
region 9 should
be shaded.
But that is not the
case for the combined Venn Diagram.
So we can conclude that
the deduction
"all cats are dogs" is not valid.
