Mathematical operation and symbol notation


Direction: In the following questions, the symbols δ, $, , @ and © are used with the meaning as indicated below.
'P $ Q' means 'P is neither equal to nor greater than Q'.
'P © Q' means 'P is neither equal to nor smaller than Q'
'P δ Q' means 'P is neither greater than nor smaller to Q'.
'P @ Q' means 'P is not smaller than Q'.
'P ∗ Q' means 'P is not greater than Q'.

in each question, three statements showing relationship, have been given , which are followed by three Conclusions I, II and III. Assuming that the given statements to be true, find out which conclusion(s) is/are definitely true.

  1. Statements
    B © N, N @ R, F ∗ R
    Conclusions
    I. B © R
    II. F ∗ N
    III. R $ B
    1. I and II are true
    2. I and III are true
    3. II and III are true
    4. I, II and III are true
    5. None of the above

  1. View Hint View Answer Discuss in Forum

    Statements
    B © N ⇒ B > N,
    N @ R ⇒ N ≥ R, F H R ⇒ F ≤ R
    So, B > N ≥ R ≥ F
    Conclusions
    I. B © R ⇒ B > R      ( true)
    II. F H N ⇒ F ≤ N       (true)
    III. R $ B ⇒ R < B       (true)

    Correct Option: D

    Statements
    B © N ⇒ B > N,
    N @ R ⇒ N ≥ R, F H R ⇒ F ≤ R
    So, B > N ≥ R ≥ F
    Conclusions
    I. B © R ⇒ B > R      ( true)
    II. F H N ⇒ F ≤ N       (true)
    III. R $ B ⇒ R < B       (true)
    So, all I, II and III are true from the given statements.


  1. Statements
    D $ M, M ∗ B, B δ J
    Conclusions
    I. J © D
    II. B @ D
    III. J @ M
    1. I and II are true
    2. I and III are true
    3. II and III are true
    4. I, II and III are true
    5. None of the above

  1. View Hint View Answer Discuss in Forum

    Statements
    D $ M ⇒ D < M,
    M H B ⇒ M ≤ B, B δ J ⇒ B = J
    So, D < M ≤ B = J
    Conclusions
    I. J © D ⇒ J > D       (true)
    II. B @ D ⇒ B ≥ D       (false)
    III. J @ M ⇒ J ≥ M       (true)

    Correct Option: B

    Statements
    D $ M ⇒ D < M,
    M H B ⇒ M ≤ B, B δ J ⇒ B = J
    So, D < M ≤ B = J
    Conclusions
    I. J © D ⇒ J > D       (true)
    II. B @ D ⇒ B ≥ D       (false)
    III. J @ M ⇒ J ≥ M       (true)
    So, Conclusion I and III are true from the given statements.



  1. Statements
    W δ K, K © F, F $ M
    Conclusions
    I. M © K
    II. W @ F
    III. F @ W
    1. Only I is true
    2. Only II is true
    3. Only III is true
    4. II and III are true
    5. None of the above

  1. View Hint View Answer Discuss in Forum

    Statements
    W δ K ⇒ W = K,
    K © F ⇒ K > F, F $ M ⇒ F < M
    So, W = K > F < M
    Conclusions
    I. M © K ⇒ M > K       (false)
    II. W @ F ⇒ W ≥ F       (false)
    III. F @ W ⇒ F ≥ w       (false)

    Correct Option: E

    Statements
    W δ K ⇒ W = K,
    K © F ⇒ K > F, F $ M ⇒ F < M
    So, W = K > F < M
    Conclusions
    I. M © K ⇒ M > K       (false)
    II. W @ F ⇒ W ≥ F       (false)
    III. F @ W ⇒ F ≥ w       (false)
    So, no conclusion is true from the given statements.


  1. Statements
    L > M,
    M > N,
    N > P.
    Conclusions
    I. L > P
    II. M > P
    1. if only Conclusion I follows
    2. if only Conclusion II follows
    3. if either Conclusion I or II follows
    4. if neither Conclusion I nor II follows
    5. if both Conclusions I and II follow

  1. View Hint View Answer Discuss in Forum

    Given that,
    L > M ....(I)
    M > N .....(II)
    N > P .....(II)
    On combining all the three statements, we get
    L > M > N > P
    Conclusions
    I. L > P     (true)
    II. M > P    (true)

    Correct Option: E

    Given that,
    L > M ....(I)
    M > N .....(II)
    N > P .....(II)
    On combining all the three statements, we get
    L > M > N > P
    Conclusions
    I. L > P     (true)
    II. M > P    (true)

    So, it is clear that both Conclusions I and II follow from the given statements.



  1. Statements
    A > B,
    B =H,
    H > G
    Conclusions
    I. A > G
    II. A > H
    1. if only Conclusion I follows
    2. if only Conclusion II follows
    3. if either Conclusion I or II follows
    4. if neither Conclusion I nor II follows
    5. if both Conclusions I and II follow

  1. View Hint View Answer Discuss in Forum

    Given that,
    A > B     .....(I)
    B = H     .....(ii)
    H > G     ...(iii)
    On combining the statement (i), (ii) and (iii), we get
    A > B = H > G
    Conclusions
     I. A > G     (true)
    II. A > H     (true)

    Correct Option: E

    Given that,
    A > B     .....(I)
    B = H     .....(ii)
    H > G     ...(iii)
    On combining the statement (i), (ii) and (iii), we get
    A > B = H > G
    Conclusions
     I. A > G     (true)
    II. A > H     (true)
    So, it is clear that both Conclusions I and II follow from the given statements.