Mathematical operation and symbol notation


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.

  1. Statements:
    J δ D, D @ N, N % F
    Conclusions:
    I. J δ F II. F © D
    1. if only conclusion I is true
    2. if only conclusion II is true
    3. if either conclusion I or II is true
    4. if neither conclusion I nor II is true
    5. if both conclusion I and II are true

  1. View Hint View Answer Discuss in Forum

    J > D ...(i) D = N ...(ii) N ≤ F ...(iii)
    From (ii) and (iii) D = N ≤ F or F ≥ D ...(iv)
    Hence II follows.
    From (i) and (iv) R and (iv) J and F can't be compared.
    Hence I does not follow.

    Correct Option: B

    J > D ...(i) D = N ...(ii) N ≤ F ...(iii)
    From (ii) and (iii) D = N ≤ F or F ≥ D ...(iv)
    Hence II follows.
    From (i) and (iv) R and (iv) J and F can't be compared.
    Hence I does not follow.


  1. Statements:
    R S J, J δ F, F % H
    Conclusions:
    I. H δ J II. R S F
    1. if only conclusion I is true
    2. if only conclusion II is true
    3. if either conclusion I or II is true
    4. if neither conclusion I nor II is true
    5. if both conclusion I and II are true

  1. View Hint View Answer Discuss in Forum

    R < J ...(i) J > F ...(ii) F ≤ H ...(iii)
    From (ii) and (iii) H and J can't be compared.
    Hence I does not follow
    From (i) and (ii) R and F can't be compared.
    Hence II does not follow

    Correct Option: D

    R < J ...(i) J > F ...(ii) F ≤ H ...(iii)
    From (ii) and (iii) H and J can't be compared.
    Hence I does not follow
    From (i) and (ii) R and F can't be compared.
    Hence II does not follow



  1. Statements:
    B @ N, N © T, T S K
    Conclusions:
    I. T @ B II. T S B
    1. if only conclusion I is true
    2. if only conclusion II is true
    3. if either conclusion I or II is true
    4. if neither conclusion I nor II is true
    5. if both conclusion I and II are true

  1. View Hint View Answer Discuss in Forum

    B = N ...(i) N ≥ T ...(ii) T > K ...(iii)
    From (i) and (ii) B = N ≥ T or T ≤ B,
    Hence I either (T = B) or II (T < B) follows

    Correct Option: C

    B = N ...(i) N ≥ T ...(ii) T > K ...(iii)
    From (i) and (ii) B = N ≥ T or T ≤ B,
    Hence I either (T = B) or II (T < B) follows


  1. Statements:
    H © T, T % M, M δ F
    Conclusions:
    I. F S T II. H δ M
    1. if only conclusion I is true
    2. if only conclusion II is true
    3. if either conclusion I or II is true
    4. if neither conclusion I nor II is true
    5. if both conclusion I and II are true

  1. View Hint View Answer Discuss in Forum

    H ≥ T ...(i) T ≤ M ...(ii) M > F ...(iii)
    From (i) and (ii) H and M can't be compared. Hence II does not follow
    From (ii) and (iii) F and T can't be compared. Hence I does not follow

    Correct Option: D

    H ≥ T ...(i) T ≤ M ...(ii) M > F ...(iii)
    From (i) and (ii) H and M can't be compared. Hence II does not follow
    From (ii) and (iii) F and T can't be compared. Hence I does not follow