Mathematical operation and symbol notation
Direction: In the following information question, the symbols @, #, % and $ are used with the following meaning as illustrated below:
'P @ Q' means 'P is not smallest than Q'.
'P # Q' means 'P is not greater than Q'.
'P % Q' means 'P is neither greater than nor equal to than Q'.
'P * Q' means 'P is neither smallest than nor greater to than Q'.
'P $ Q' means 'P is neither smallest than nor greater to than Q'.
Now each of the following questions assuming the given statement to be true, find which of the three conclusions I, II and III given them is are definitely true and give your answer accordingly.
 Statements:
I # N
Conclusions:
I. J % T II. T S N III. N @ J

 None follow
 Only I and II follow
 Only I and III follow
 Only II and III follow
 All follow

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J ≤ N ...(i) K ≤ N ...(ii) T > K ...(iii)
Combining these we get T > K ≥ N ≥ J
Hence J < T and I follows. Also T > N and II follows.
Beside N ≥ J and III followsCorrect Option: E
J ≤ N ...(i) K ≤ N ...(ii) T > K ...(iii)
Combining these we get T > K ≥ N ≥ J
Hence J < T and I follows. Also T > N and II follows.
Beside N ≥ J and III follows
 Statements:
M % R, R # T, T * N
Conclusions:
I. N * R, II. NSR, II. NSM

 All follow
 Only either I or II follows
 Only either I or II and III follow
 Only either I or III and II follow
 None of these

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M < R ...(i) R ≤ T ...(ii) T = N ...(iii)
Combining these we get M < R ≤ T = N
Hence N ≤ R
Which means either I (N = R) or II (N > R) follows.
Again N > M. Hence III followsCorrect Option: C
M < R ...(i) R ≤ T ...(ii) T = N ...(iii)
Combining these we get M < R ≤ T = N
Hence N ≤ R
Which means either I (N = R) or II (N > R) follows.
Again N > M. Hence III follows
Direction: In the following information question, the symbols @, ©, S, % and are used with the following meaning as illustrated below:
'P © Q' means 'P is either greater than or equal to Q'.
'P % Q' means 'P is either smallest than or equal to Q'.
'P @ Q' means 'P is neither smallest than nor greater to than Q'.
'P S Q' means 'P is smallest than Q'.
'P δ Q' means 'P is greater than Q'.
Now each of the following questions assuming the given statement to be true, find which of the three conclusions I and II given below them is are definitely true.
 Statements:
M % R, R S T, T © K
Conclusions:
I. T δ M II. R S T

 if only conclusion I is true
 if only conclusion II is true
 if either conclusion I or II is true
 if neither conclusion I nor II is true
 if both conclusion I and II are true

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M ≤ R ...(i) R < T ...(ii) T ≥ K ...(iii)
From (ii) and (iii) M ≤ R < T or T > M
Hence I follows
From (ii) and (iii) R and K can't be compared. Hence II does not followCorrect Option: A
M ≤ R ...(i) R < T ...(ii) T ≥ K ...(iii)
From (ii) and (iii) M ≤ R < T or T > M
Hence I follows
From (ii) and (iii) R and K can't be compared. Hence II does not follow
 Statements:
W % V, V @ Z, Z © D
Conclusions:
I. D % V II. W % Z

 if only conclusion I is true
 if only conclusion II is true
 if either conclusion I or II is true
 if neither conclusion I nor II is true
 if both conclusion I and II are true

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W ≤ V ..(i) V = Z ...(ii) Z ≥ D ...(iii)
From (ii) and (iii) V = Z ≥ D or D ≤ V
Hence I follows.
From (i) and (ii) W ≤ V = Z or W ≤ Z
Hence II follows.Correct Option: E
W ≤ V ..(i) V = Z ...(ii) Z ≥ D ...(iii)
From (ii) and (iii) V = Z ≥ D or D ≤ V
Hence I follows.
From (i) and (ii) W ≤ V = Z or W ≤ Z
Hence II follows.
 Statements:
B δ T, T S H, H @ M
Conclusions:
I. M δ T II. B δ H

 if only conclusion I is true
 if only conclusion II is true
 if either conclusion I or II is true
 if neither conclusion I nor II is true
 if both conclusion I and II are true

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B > T ...(i) T < H ...(ii) H = M ...(iii)
From (ii) and (iii) T < H = M or M > I
Hence I follow
From (i) and (ii) B and H can't be compared. Hence II does not followCorrect Option: A
B > T ...(i) T < H ...(ii) H = M ...(iii)
From (ii) and (iii) T < H = M or M > I
Hence I follow
From (i) and (ii) B and H can't be compared. Hence II does not follow