UPSC Prelims 2023·CSAT·Logical Reasoning·Deductive Logic

Consider the following statements in respect of five candidates P, Q, R, S and T. Two statements are true and one statement is false. True Statement: One of P and Q was selected for the job. False Statement: At least one of R and S was selected for the job. True Statement: At most two of R, S and T were selected for the job. Which of the following conclusions can be drawn? 1. At least four were selected for the job. 2. S was selected for the job. Select the correct answer using the code given below:

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  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2Correct

Explanation

Let's break down the statements: 1. True Statement: "One of P and Q was selected for the job." This means exactly one person from P and Q is selected. (P XOR Q) 2. False Statement: "At least one of R and S was selected for the job." Since this statement is FALSE, its negation must be TRUE. The negation is: "Neither R nor S was selected for the job." Therefore, R was NOT selected, and S was NOT selected. 3. True Statement: "At most two of R, S and T were selected for the job." From point 2, we know R was NOT selected and S was NOT selected. Substituting this into statement 3: "At most two of (not selected), (not selected) and T were selected." This simplifies to: "At most one of T was selected." (Since T is a single person, either T is selected or not). So, T can be selected or T can be not selected. Now let's evaluate the conclusions: Conclusion 1: "At least four were selected for the job." * From {P, Q}: Exactly 1 person is selected. * From {R, S}: 0 persons are selected (R and S are not selected). * From {T}: 0 or 1 person is selected. Total selected candidates = (1 from P/Q) + (0 from R/S) + (0 or 1 from T) = 1 or 2. Since the maximum number of selected candidates is 2, the statement "At least four were selected for the job" is FALSE. Conclusion 2: "S was selected for the job." From point 2, we definitively concluded that S was NOT selected for the job. Therefore, this conclusion is FALSE. Since both Conclusion 1 and Conclusion 2 are false, the correct answer is D) Neither 1 nor 2.
Logical Reasoning: Consider the following statements in respect of five candidates P, Q, R, S and T. Two statements are true and one statem

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