Three statements are given, followed by Three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.Statements:No number is a machine.Not a single machine is a bowl.Every bowl is a sink. Conclusions:(I) Some sinks which are bowls are numbers as well.(II) No number is a bowl.(III) Some sinks are bowls.

Let's analyze the assertions using set relations: "Every bowl is a sink" $⟹$ All bowls are subset inside sinks. Hence, the intersection between sinks and bowls is definitely non-empty. Thus, Conclusion III ("Some sinks are bowls") definitely follows."No number is a machine" and "Not a single machine is a bowl" provide zero direct constraints restricting intersection links between numbers and bowls. Thus, a bowl can optionally overlap with numbers or remain separated.Since the relation between numbers and bowls is unknown, Conclusion I ("Some sinks which are bowls are numbers as well") and Conclusion II ("No number is a bowl") cannot be determined with absolute certainty. Let's see if they form an either-or pair: Conclusion I demands some bowls are numbers, while Conclusion II demands no number is a bowl. Since they cover all possibilities for the relationship between numbers and bowls, either conclusion I or II must be true.Therefore, Conclusion III follows along with either conclusion I or II. Looking at the given options, option A states "Only conclusions II and III follow", and option D states "Only conclusion III follows". Since either-or is not combined with III in the options, let's verify if only III fits as a standalone guaranteed conclusion. Yes, Conclusion III is absolutely true independently.