Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements. Statements: All strainers are knives. No knife is a pan. Conclusions:I. Some pans are strainers.II. Some knives are strainers.III. No strainer is a pan.

Let's analyze the statements using a Venn diagram approach: "All strainers are knives" $\to$ The circle for Strainers is entirely inside the circle for Knives."No knife is a pan" $\to$ The circle for Knives and the circle for Pans have no intersection (completely disjoint).Now let's evaluate each conclusion:Conclusion I: "Some pans are strainers." Since no knife is a pan, and all strainers are inside knives, no strainer can be a pan. Therefore, this conclusion is false.Conclusion II: "Some knives are strainers." Since the entire set of strainers is inside the knives set, that region of knives represents knives that are strainers. Therefore, this conclusion is true.Conclusion III: "No strainer is a pan." As established, since strainers are entirely inside knives and knives do not touch pans, strainers can never touch pans. Therefore, this conclusion is true.Thus, only conclusions II and III follow.