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











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    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











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    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











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    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











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    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











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    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.