Mathematical operation and symbol notation


Direction: In these following question, the symbols @, S, #, * and % are used with the different meaning as follow:
'A @ B' means 'A is smallest than B'.
'A S B' means 'A is greater than B'.
'A # B' means 'A is either smallest than or equal to B.
'A * B' means 'A is either greater than or equal to B.
'A % B' means 'A is either smallest than nor greater 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 S I, I * M, M # Q
    Conclusions:
    I. I # Q II. I * Q
    1. if only conclusion I is true
    2. if only conclusion I 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 > I ...(i) I ≥ M ...(ii) M ≤ Q ...(iii)
    From (ii) and (iii) I and Q, can't be compared. But I and II make a complementary pair. Hence either I (I ≤ Q) or II (I ≥ Q) follows.

    Correct Option: C

    V > I ...(i) I ≥ M ...(ii) M ≤ Q ...(iii)
    From (ii) and (iii) I and Q, can't be compared. But I and II make a complementary pair. Hence either I (I ≤ Q) or II (I ≥ Q) follows.


  1. Statements:
    H # T, T @ L, L % F
    Conclusions:
    I. F S H II. H # L
    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 ≤ T ...(i) T < L ...(ii) L = F ...(iii)
    Combining these we get H ≤ T < L = F.
    Hence F > H and I follows.
    But H < L and Hence II (H ≤ L ) does not follow.

    Correct Option: A

    H ≤ T ...(i) T < L ...(ii) L = F ...(iii)
    Combining these we get H ≤ T < L = F.
    Hence F > H and I follows.
    But H < L and Hence II (H ≤ L ) does not follow.



  1. Statements:
    H ≥ G < I; F ≤ G > Z
    Conclusions:
    I. F ≤ H II. Z < I
    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 ≥ G < I; F ≤ G > Z
    Check for I:
    F ≤ G ≤ H is definitely follows
    Check for II:
    Z < G < I
    ∴ Z < I also follows
    Hence, both I and II follows

    Correct Option: E

    H ≥ G < I; F ≤ G > Z
    Check for I:
    F ≤ G ≤ H is definitely follows
    Check for II:
    Z < G < I
    ∴ Z < I also follows
    Hence, both I and II follows


  1. Conclusions:
    I. R ≥ S II. W < G
    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

    S ≤ T < U ≥ W; T ≤ R, G > U
    Check for I:
    S ≤ T ≤ R
    ∴ R ≥ S follows
    Check for II:
    G > U ≥ W
    ∴ W < G follows
    Hence, both I and II follows

    Correct Option: E

    S ≤ T < U ≥ W; T ≤ R, G > U
    Check for I:
    S ≤ T ≤ R
    ∴ R ≥ S follows
    Check for II:
    G > U ≥ W
    ∴ W < G follows
    Hence, both I and II follows



  1. Statements:
    C ≥ D = E ≤ F; Y < D ≥ W
    Conclusions:
    I. C ≥ Y II. F ≥ Y
    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

    C ≥ D = E ≤ F, Y < D ≥ W
    Check for I:
    C ≥ D > Y
    It means C > Y. Thus, I does stand true. check for II:
    Y < D ≤ F
    It means F > Y. Thus, II also does not stand true.

    Correct Option: D

    C ≥ D = E ≤ F, Y < D ≥ W
    Check for I:
    C ≥ D > Y
    It means C > Y. Thus, I does stand true. check for II:
    Y < D ≤ F
    It means F > Y. Thus, II also does not stand true.