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### Logical Reasoning :: Mathematical and Computer Operations

1. In the following questions, the symbols @, #, $, % and © are used with the following meaning as illustrated below: 'P$Q' means 'P is not greater than Q'.
'P@Q' means 'P is neither smaller than nor equal to Q'.
'P%Q' means 'P is neither greater than not equal to Q'.
'P©Q' means 'P is not smaller than Q'.
'P#Q' means 'P is neither greater than nor smaller than Q'.
Now in each of the following questions assuming the given statements to be true, find which of the three conclusions I, II and III given below them is are definitely true.

Statements: M @ R, R © K, J % K
Conclusions: I. M @ J  II. J % R  III. K % M
2.  A. None follows B. Only either I or II follows C. Only either II or III follows D. Only II and III follows E. All follow   3. In the following questions, the symbols @, #, $, % and © are used with the following meaning as illustrated below: 'P$Q' means 'P is not greater than Q'.
'P@Q' means 'P is neither smaller than nor equal to Q'.
'P%Q' means 'P is neither greater than not equal to Q'.
'P©Q' means 'P is not smaller than Q'.
'P#Q' means 'P is neither greater than nor smaller than Q'.
Now in each of the following questions assuming the given statements to be true, find which of the three conclusions I, II and III given below them is are definitely true.

Statements: D © N, N # V, W $V Conclusions: I. D # W II. W % D III. V # 4.  A. None follows B. Only either I or II follows C. Only either II or III follows D. Only either II or III and I follow E. All follow   5. In the following questions, the symbols @, #,$, % and © are used with the following meaning as illustrated below:
'P$Q' means 'P is not greater than Q'. 'P@Q' means 'P is neither smaller than nor equal to Q'. 'P%Q' means 'P is neither greater than not equal to Q'. 'P©Q' means 'P is not smaller than Q'. 'P#Q' means 'P is neither greater than nor smaller than Q'. Now in each of the following questions assuming the given statements to be true, find which of the three conclusions I, II and III given below them is are definitely true. Statements: H % B, M © B, K # M Conclusions: I. K @ H II. B # K III. K @ B 6.  A. All follow B. Only I follows C. Only either II or III follows D. Only either II or III and I follows E. None of these   7. In the following questions, the symbols @, #,$, % and © are used with the following meaning as illustrated below:
'P$Q' means 'P is not greater than Q'. 'P@Q' means 'P is neither smaller than nor equal to Q'. 'P%Q' means 'P is neither greater than not equal to Q'. 'P©Q' means 'P is not smaller than Q'. 'P#Q' means 'P is neither greater than nor smaller than Q'. Now in each of the following questions assuming the given statements to be true, find which of the three conclusions I, II and III given below them is are definitely true. Statements: V © M, N % V, J @ N Conclusions: I. J @ M II. M @ N III. V @ J 8.  A. None follows B. Only I follows C. Only either I or II follows D. Only III follows E. All follows   9. In the following questions, the symbols @, #,$, % and © are used with the following meaning as illustrated below:
'P$Q' means 'P is not greater than Q'. 'P@Q' means 'P is neither smaller than nor equal to Q'. 'P%Q' means 'P is neither greater than not equal to Q'. 'P©Q' means 'P is not smaller than Q'. 'P#Q' means 'P is neither greater than nor smaller than Q'. Now in each of the following questions assuming the given statements to be true, find which of the three conclusions I, II and III given below them is are definitely true. Statements: T # R, R$ W, W % H
Conclusions: I. H @ R II. H @ T III. H © T
10.  A. Only I follows B. Only II follows C. Only I and II follows D. All follows E. None of these   11. If 'P' denotes 'divided by'; 'Q' denotes 'added to'; 'M' denotes 'subtracted from'; 'B' denotes 'multiplied by'; then
1 8 B 1 2 P 4 M 8 Q 6 = ?
12.  A. 108 B. 46 C. 17 D. 52 E. None of these   13. In these questions, the symbols @, *, $, # and % are used with the following meanings as illustrated below: 'P@Q' means 'P is not smaller than Q'. 'P#Q' means 'P is not greater than q'. 'P%Q' means 'P is neither smaller than nor greater than Q'. 'P$Q' means 'P is neither smaller than nor equal to Q'.

Statements: T % B, M * B, J # B
Conclusions: I. T % M   II. T % J
14.  A. if only conclusion I is true. B. if only conclusion II is true. C. if either conclusion I or II is true. D. if neither conclusion I nor II is true. E. if both the conclusions I and II are true.   15. In these questions, the symbols @, *, $, # and % are used with the following meanings as illustrated below: 'P@Q' means 'P is not smaller than Q'. 'P#Q' means 'P is not greater than q'. 'P%Q' means 'P is neither smaller than nor greater than Q'. 'P$Q' means 'P is neither smaller than nor equal to Q'.

Statements: V # D, D * K, F $K Conclusions: I. D @ F II. V @ F 16.  A. if only conclusion I is true. B. if only conclusion II is true. C. if either conclusion I or II is true. D. if neither conclusion I nor II is true. E. if both the conclusions I and II are true.   17. In these questions, the symbols @, *,$, # and % are used with the following meanings as illustrated below:
'P@Q' means 'P is not smaller than Q'.
'P#Q' means 'P is not greater than q'.
'P%Q' means 'P is neither smaller than nor greater than Q'.
'P$Q' means 'P is neither smaller than nor equal to Q'. Statements: W # D, D % M, M * F Conclusions: I. D @ F II. F % D 18.  A. if only conclusion I is true. B. if only conclusion II is true. C. if either conclusion I or II is true. D. if neither conclusion I nor II is true. E. if both the conclusions I and II are true.   19. In these questions, the symbols @, *,$, # and % are used with the following meanings as illustrated below:
'P@Q' means 'P is not smaller than Q'.
'P#Q' means 'P is not greater than q'.
'P%Q' means 'P is neither smaller than nor greater than Q'.
'P$Q' means 'P is neither smaller than nor equal to Q'. Statements: H * R, R$ N, N @ K
Conclusions: I. H @ K   II. K \$ R
20.  A. if only conclusion I is true. B. if only conclusion II is true. C. if either conclusion I or II is true. D. if neither conclusion I nor II is true. E. if both the conclusions I and II are true.   