Mathematical operation and symbol notation


Direction: In these following question, the symbols @, #,* and % are used with the different meaning as follow:
'A @ B' means 'A is not smallest than B'
'A # B' means 'A is neither smallest than nor equal to B.
'A S B' means 'A is neither than nor smallest than B.
'A * B' means "A is not greater than B'.
'A % B' means 'A is neither greater than or equal to B'
In each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true.

  1. Statements:
    V * W, W S H, H @ I
    Conclusions:
    I. L * V II. L S D
    1. if only conclusion I is true
    2. if only conclusion II is true
    3. if either conclusion I or conclusion II is true
    4. if neither conclusion I nor conclusion II is true
    5. if both conclusion I and II are true

  1. View Hint View Answer Discuss in Forum

    V ≤ W ...(i) W = H ...(ii) H ≥ I ...(iii)
    From (i) and (ii) W = H ≥ I or W ≥ I ...(iv)
    Hence I ≤ W and II follows But V and I can't be compared From (iii) and (iv)
    Hence I does not follows.

    Correct Option: B

    V ≤ W ...(i) W = H ...(ii) H ≥ I ...(iii)
    From (i) and (ii) W = H ≥ I or W ≥ I ...(iv)
    Hence I ≤ W and II follows But V and I can't be compared From (iii) and (iv)
    Hence I does not follows.


  1. Statements:
    L * P, P % V, V # D
    Conclusions:
    I. L * V II. L S D
    1. if only conclusion I is true
    2. if only conclusion II is true
    3. if either conclusion I or conclusion II is true
    4. if neither conclusion I nor conclusion II is true
    5. if both conclusion I and II are true

  1. View Hint View Answer Discuss in Forum

    L ≤ P.....(i) P < V ...(ii) V > D ...(iii)
    Combining (i) and (ii)
    we get L ≤ P < V or L < W ...(iv) L and D can't be compared
    Hence II does not follows

    Correct Option: D

    L ≤ P.....(i) P < V ...(ii) V > D ...(iii)
    Combining (i) and (ii)
    we get L ≤ P < V or L < W ...(iv) L and D can't be compared
    Hence II does not follows



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.

  1. Statements:
    V @ M, A S M, R # V
    Conclusions:
    I. R # A II/. V @ A III. R S M
    1. Only I follows
    2. Only II follows
    3. Only III follows
    4. None follows
    5. All follow

  1. View Hint View Answer Discuss in Forum

    V ≥ M ...(i) A > M ...(ii) R ≤ V ...(iii)
    These lead us to no relationship by combination.

    Correct Option: D

    V ≥ M ...(i) A > M ...(ii) R ≤ V ...(iii)
    These lead us to no relationship by combination.


  1. Statements:
    T S K, K # R, R * M
    Conclusions:
    I. M * K II. M % T III. M S K
    1. All follow
    2. Only either I and III follows
    3. Only either I and II follows
    4. Only either II and III follows
    5. None of these

  1. View Hint View Answer Discuss in Forum

    D > K ...(i) K ≤ R ...(ii) R = M ...(iii)
    From (ii) and (iii) M ≥ K ...(iv)
    Hence either I (M = K) or III (M > K) follow. But M and T can't be compared from (i) and (iv).
    Hence II does not follow.

    Correct Option: B

    D > K ...(i) K ≤ R ...(ii) R = M ...(iii)
    From (ii) and (iii) M ≥ K ...(iv)
    Hence either I (M = K) or III (M > K) follow. But M and T can't be compared from (i) and (iv).
    Hence II does not follow.



  1. Statements:
    B * D, D @ H, H % F
    Conclusions:
    I. B * F II B S F III. D S F
    1. None follow
    2. Only either I or III follows
    3. Only either I or II follows
    4. Only either II or III follows
    5. All follow

  1. View Hint View Answer Discuss in Forum

    B = D ...(i) D ≥ H ...(ii) H > F ...(iii)
    D and F can't be compared from (i) and (ii). And from the same reason, if we bear (i) an mind. B and F can't be compared. Hence none follows.

    Correct Option: A

    B = D ...(i) D ≥ H ...(ii) H > F ...(iii)
    D and F can't be compared from (i) and (ii). And from the same reason, if we bear (i) an mind. B and F can't be compared. Hence none follows.