Mathematical operation and symbol notation


Direction: In the following information question, the symbols @, ©, %, S and δ are used with the following meaning as illustrated below:
'P % Q' means 'P is greater than Q'
'P δ Q' means 'P is neither greater than smallest than Q'
'P @ Q' means 'P is smallest than Q'.
'p © Q' means 'P is either smallest than or equal to Q'
'P S Q' means 'P is either greater than or equal to 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. Statement :
    M @ J, J © R, R δ K
    Conclusion :
    I. K δ J II. K % J
    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 < J ...(i) J≤ R ...(ii) R = K .....(iii)
    From (ii) and (iii) J ≤ K or K ≥ J, .....(iv)
    Hence either I (K = J) or II (K > J) follow

    Correct Option: C

    M < J ...(i) J≤ R ...(ii) R = K .....(iii)
    From (ii) and (iii) J ≤ K or K ≥ J, .....(iv)
    Hence either I (K = J) or II (K > J) follow


  1. Statements:
    V % B, B S D , D © E
    Conclusions:
    I. E δ B II. D @ V
    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 > B ...(i) B ≥ D ...(ii) D &Le; E ...(iii)
    From (ii) and (iii) E and B can't be compared.
    Hence I does not follows. From (i) and (iv) V > D or D < V
    Hence II follows

    Correct Option: A

    V > B ...(i) B ≥ D ...(ii) D ≤ E ...(iii)
    From (ii) and (iii) E and B can't be compared.
    Hence I does not follows. From (i) and (iv) V > D or D < V
    Hence II follows



  1. Statements: H S N, N % R, R @ J
    Conclusions:I. R @ H II. J % 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 ≥ N ....(i) N > R ....(ii) R < J ...(iii)
    From (i) and (ii) R > H ...(iv)
    Hence R < H and I follows
    But J and H can't compared From (iii) and (iv)
    Hence II does not follow.

    Correct Option: A

    H ≥ N ....(i) N > R ....(ii) R < J ...(iii)
    From (i) and (ii) R > H ...(iv)
    Hence R < H and I follows
    But J and H can't compared From (iii) and (iv)
    Hence II does not follow.


  1. Statement :
    F δ T, T S M, M © R
    Conclusion :
    I. R S F II. M © 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 = T ....(i) T ≥ M ....(ii) M ≤ R .....(iii)
    From (i) and (ii) F ≥ M ....(iv)
    Hence M ≤ F and II follows
    But R and F can't be compared From (iii) and (iv)
    Hence I does not follow

    Correct Option: B

    F = T ....(i) T ≥ M ....(ii) M ≤ R .....(iii)
    From (i) and (ii) F ≥ M ....(iv)
    Hence M ≤ F and II follows
    But R and F can't be compared From (iii) and (iv)
    Hence I does not follow



  1. Statement :
    W © D, D S B, B @ H
    Conclusion :
    I. H % D II. W @ B
    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

    W ≤ D ....(i) D ≥ B .....(ii) B > H ... (iii)
    H and D can't be compared from (ii) and (iii)
    Hence; I does not follows
    Nor can W and B he be compared From (i) and (ii).
    Hence II does not follows

    Correct Option: D

    W ≤ D ....(i) D ≥ B .....(ii) B > H ... (iii)
    H and D can't be compared from (ii) and (iii)
    Hence; I does not follows
    Nor can W and B he be compared From (i) and (ii).
    Hence II does not follows