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Negative–negative syllogism analysis: Using 'No bat is ball' and 'No ball is wicket', determine whether (I) 'No bat is wicket' and (II) 'All wickets are bats' follow with logical certainty.

Difficulty: Medium

Correct Answer: Neither I nor II follows

Explanation:

Given data

  • Premise 1: No bat is ball (Bat ∩ Ball = ∅).
  • Premise 2: No ball is wicket (Ball ∩ Wicket = ∅).
  • Test: (I) No bat is wicket. (II) All wickets are bats.

Concept/Approach

Two negative premises about the same middle term (Ball) do not establish any relation between the two end terms (Bat and Wicket). A Venn check or counterexample settles necessity.

Step-by-step evaluation

1) Both statements forbid overlap with Ball, but say nothing about Bat–Wicket overlap.2) It remains possible that some bats are wickets (or none are), i.e., relation is undetermined.3) (II) is an extreme universal claim with no support.

Verification/Alternative

Countermodel: Let Bat = {b1}, Wicket = {b1}, Ball = {c1}. Then premises hold (neither Bat nor Wicket intersects Ball), but (I) is false and (II) is false. Hence neither conclusion is compelled.

Common pitfalls

  • Illicit inference 'No bat is wicket' merely because both avoid Ball.

Final Answer
Neither I nor II follows.

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