Mathematical operation and symbol notation


Direction: In the following information question, the symbol #, %, @, S and © are used with the following meaning as illustrated below:
'P # Q' means 'P is smallest than Q'.
'P % Q' means 'P is not greater Q'.
'P @ Q' means 'P is neither smallest than nor equal to Q'.
'P S Q' means 'P is neither greater than nor equal to Q'.
'P © Q' means 'P is neither smallest than greater nor greater than Q'.
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:
    H © W, W % R, R @ F
    Conclusions:
    I. R © H II. R @ H
    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

    H = W ...(i) W ≤ R ...(ii) R > F ...(iii)
    From (i) and (ii) H = W ≤ R or R ≥ H, Hence either I (R = H) or II (R > H) follows.

    Correct Option: C

    H = W ...(i) W ≤ R ...(ii) R > F ...(iii)
    From (i) and (ii) H = W ≤ R or R ≥ H, Hence either I (R = H) or II (R > H) follows.


  1. Statements:
    M S T, T @ K, K © D
    Conclusions:
    I. D S T II. K S M
    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

    M < T ... (i) T > K ...(ii) K = D ...(iii)
    From (ii) and (iii) T > K = D or D < T.
    Hence I follow
    From (i) and (ii) K and M can't be compared
    Hence II does not follow

    Correct Option: A

    M < T ... (i) T > K ...(ii) K = D ...(iii)
    From (ii) and (iii) T > K = D or D < T.
    Hence I follow
    From (i) and (ii) K and M can't be compared
    Hence II does not follow



  1. Statements:
    H @ W, W S M, M # K
    Conclusions:
    I. K S W II. H @ M
    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

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

    Correct Option: D

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


  1. Statements:
    F # K, K S B, B % M
    Conclusions:
    I. M @ F II. B @ F
    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

    F ≥ K ...(i) K > B ....(ii) B ≤ M ...(iii)
    From (i) and (ii) F can't be compared with B and consequently with M. Hence neither II nor I follows.

    Correct Option: D

    F ≥ K ...(i) K > B ....(ii) B ≤ M ...(iii)
    From (i) and (ii) F can't be compared with B and consequently with M. Hence neither II nor I follows.



  1. Statements:
    R # T, T © M, M @ D
    Conclusions:
    I. D S T II. R # M
    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

    R ≥ T ...(i) T = M ...(ii) M > D ...(iii)
    Combining these we get R ≥ T = M > D.
    Hence D > T and I follows.
    Also R J≥ T and II follows.

    Correct Option: E

    R ≥ T ...(i) T = M ...(ii) M > D ...(iii)
    Combining these we get R ≥ T = M > D.
    Hence D > T and I follows.
    Also R J≥ T and II follows.