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.
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 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.
Solution
Given the statements:
- A ⋆ B (A is not greater than B, i.e., A ≤ B)
- B # C (B is neither smaller than nor greater than C, i.e., B = C)
- C & D (C is greater than D, i.e., C > D)
- D © E (D is either greater than or equal to E, i.e., D ≥ E)
Now, let's analyze the conclusions:
I. E © A (E is either greater than or equal to A, i.e., E ≥ A)
- From A ⋆ B, we have A ≤ B.
- From B # C, we have B = C.
- From C & D, we have C > D, which implies B > D.
- From D © E, we have D ≥ E, which implies E ≤ D.
- Combining these, we get A ≤ B = C > D ≥ E, which implies A ≤ E. Therefore, E ≥ A.
Conclusion I is true.
II. B & E (B is greater than E, i.e., B > E)
- From the above analysis, we have B = C > D ≥ E.
- Therefore, B > E.
Conclusion II is true.
III. D # B (D is neither smaller than nor greater than B, i.e., D = B)
- From the above analysis, we have B = C > D.
- Therefore, D ≠ B.
Conclusion III is not true.
Based on the analysis, the correct option is:
Both Conclusions I and II are 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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In the figure below, =m∠3134°. Find m∠1, m∠2, and m∠4.
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