Statements : Some hens are cows. All cows are horses. Conclusions : I. Some horses are hens. II. Some hens are horses.

Only conclusion I follows
Only conclusion II follows
Either I or II follows
Neither I nor II follows E. Both I and II follow

The correct answer is: Only conclusion II follows.

The first statement is in the form “Some $A$ are $B$.” The second statement is in the form “All $B$ are $C$.” We can use the following rule of inference to draw a conclusion:

  • If some $A$ are $B$, and all $B$ are $C$, then some $A$ are $C$.

In this case, we have $A = \text{hens}, B = \text{cows}, C = \text{horses}$. Therefore, we can conclude that “Some hens are horses.”

We cannot conclude that “Some horses are hens.” This is because the second statement does not tell us anything about whether or not all $C$ are $A$. It is possible that there are some $C$ that are not $A$. For example, all squares are rectangles, but not all rectangles are squares. Therefore, we cannot conclude that “Some horses are hens” just because we know that some hens are cows and all cows are horses.

In conclusion, only conclusion II follows.