Venn Diagram Solution


We have the following premises and associated Venn Diagrams:





"All dogs are mammals."




"All cats are mammals."
Combining the Venn Diagrams for the above premises, 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.
.

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