Statements :

No dog is a cat.

All cats are mats.

Conclusions :

I. Some dogs are mats.

II. All dogs can never be mats.

(i) All flowers are thorns $o$ Universal Affirmative (A–type). (ii) Some plugs are tablets $o$ Particular Affirmative (I–type). (iii) No tablet is a door $o$ Universal Negative (E–type). (iv) Some tablets are not doors $o$ Particular Negative (O–type). E + A $Rightarrow$ O₁–type of Conclusion “Some mats are not dogs.” Venn diagrams of “Some mats are not dogs” : Or

Venn diagram II contradicts the Conclusion II.

Thus, neither Conclusion I nor Conclusion II follows.