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 pharmacists are statisticians. Some statisticians are mathematicians. Conclusions: I. All pharmacists are mathematicians. II. Some pharmacists are mathematicians. III. Some mathematicians are statisticians. IV. Some statisticians are pharmacists. Correct Answer Both conclusions III and IV follow. The least possible Venn diagram for the given statements is as shown below :- [ alt="F1 Savita Railways 17.05.2022 D36" src="//storage.googleapis.com/tb-img/production/22/05/F1_Savita_Railways_17.05.2022_D36.png" style="width: 344px; height: 104px;"> Conclusions: I. All pharmacists are mathematicians → False (As All pharmacists are statisticians and Some statisticians are mathematicians so, All pharmacists are mathematicians, hence, false) II. Some pharmacists are mathematicians → False (As All pharmacists are statisticians and Some statisticians are mathematicians so, Some pharmacists are mathematicians hence, false) III. Some mathematicians are statisticians → True (As Some statisticians are mathematicians so, Some mathematicians are statisticians it is definitely true) IV. Some statisticians are pharmacists → True (As All pharmacists are statisticians so, Some statisticians are pharmacists it is definitely true) ∴ Here, Conclusions III and IV are true. Hence, the correct answer is "Both conclusions III and IV follow".