Statements: No bat is ball. No ball is wicket. Conclusions: I. No bat is…

Concept

In syllogisms, when both premises are negative (No X is Y type statements), no valid conclusion can be drawn connecting the two end terms. A negative premise only tells us that two classes do not overlap; it gives no information about how those classes relate to a third class through that negative link. Two negative statements sharing a common middle term can never be combined into a definite conclusion about the remaining two terms.

Application

Statement 1, "No bat is ball," is a universal negative (E-type) statement: the Bat and Ball classes are wholly disjoint. Statement 2, "No ball is wicket," is also a universal negative (E-type) statement: the Ball and Wicket classes are wholly disjoint.

Both premises are negative and share only the middle term "ball." Since the rule of exclusive premises forbids a valid conclusion whenever both premises are negative, no definite relationship between "bat" and "wicket" can be deduced from these two statements alone.

Cross-check

Two different arrangements of bat, ball, and wicket that both satisfy the given statements confirm this:

• Case 1: let bat and wicket be the same class (bat = {p, q}, wicket = {p, q}, ball = {r}). Both statements still hold, but here "No bat is wicket" is false and "All wickets are bats" is true.

• Case 2: let bat and wicket be disjoint classes (bat = {p}, wicket = {q}, ball = {r}). Both statements still hold, but here "No bat is wicket" is true and "All wickets are bats" is false.

Since each case satisfies both premises yet gives opposite truth values for Conclusion I and Conclusion II, neither conclusion follows with certainty.

Answer

Because both premises are negative, neither Conclusion I nor Conclusion II can be validly drawn from them.