Directions: In the following questions, the symbols ⋆, &, @, ©, and # are used with the following meaning as illustrated below: ‘A @ B’ means ‘A is neither greater than nor equal to B’. ‘A # B’ means ‘A is neither smaller than nor greater than B’. ‘A * B’ means ‘A is not greater than B’. ‘A & B’ means ‘A is greater than B’. ‘A © B’ means ‘A is either greater than or equal to B’. Now, In the following question assuming the given statements to be true, find which of the conclusions I, II & III given below them is/are definitely true? Statements: M & P, P © Q, Q * R, R @ S Conclusions: I. S # M II. P © R III. Q @ S Options Both Conclusions I and II are true. Both Conclusions I and III are true. Only Conclusion III is true. Either Conclusion I or III is true. Neither Conclusion I nor III is true.
Question
Directions: In the following questions, the symbols ⋆, &, @, ©, and # are used with the following meaning as illustrated below: ‘A @ B’ means ‘A is neither greater than nor equal to B’. ‘A # B’ means ‘A is neither smaller than nor greater than B’. ‘A * B’ means ‘A is not greater than B’. ‘A & B’ means ‘A is greater than B’. ‘A © B’ means ‘A is either greater than or equal to B’. Now, In the following question assuming the given statements to be true, find which of the conclusions I, II & III given below them is/are definitely true? Statements: M & P, P © Q, Q * R, R @ S Conclusions: I. S # M II. P © R III. Q @ S
Options Both Conclusions I and II are true.
Both Conclusions I and III are true.
Only Conclusion III is true.
Either Conclusion I or III is true.
Neither Conclusion I nor III is true.
Solution
Let's analyze the given statements and conclusions step by step.
Statements:
- M & P: M is greater than P.
- P © Q: P is either greater than or equal to Q.
- Q * R: Q is not greater than R, which means Q is either smaller than or equal to R.
- R @ S: R is neither greater than nor equal to S, which means R is smaller than S.
Conclusions:
- S # M: S is neither smaller than nor greater than M, which means S is equal to M.
- P © R: P is either greater than or equal to R.
- Q @ S: Q is neither greater than nor equal to S, which means Q is smaller than S.
Step-by-Step Analysis:
- From M & P (M > P) and P © Q (P ≥ Q), we can infer that M > Q.
- From Q * R (Q ≤ R), we can infer that M > R.
- From R @ S (R < S), we can infer that M > S.
Conclusion Analysis:
- S # M: S = M. This is not true because we have M > S.
- P © R: P ≥ R. From P ≥ Q and Q ≤ R, we cannot definitively conclude P ≥ R.
- Q @ S: Q < S. This is true because Q ≤ R and R < S, so Q < S.
Final Answer: Only Conclusion III is true.
Options: Only Conclusion III is true.
Similar Questions
Which of the following symbols is used to mark a conclusion?¬→∨∴
Directions: In the following questions, the symbols ⋆, &, @, ©, and # are used with the following meaning as illustrated below: ‘A @ B’ means ‘A is neither greater than nor equal to B’. ‘A # B’ means ‘A is neither smaller than nor greater than B’. ‘A ⋆ B’ means ‘A is not greater than B’. ‘A & B’ means ‘A is greater than B’. ‘A © B’ means ‘A is either greater than or equal to B’. Now in each of the following questions assuming the given statements to be true, find which of the two conclusions I, II & III given below them is/are definitely true? Statements: A ⋆ B, B # C, C & D, D © E Conclusions: I. E © A II. B & E III. D # B Options Both Conclusions I and II are true. Both Conclusions I and III are true. Only Conclusion III is true. Either Conclusion I or III is true. Neither Conclusion I nor III is true.
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