Mathematical operation and symbol notation


Direction: In the following questions, the symbols @, $, #, © and % are used with the following meanings as illustrated below.
'P $ Q' means 'P is not smaller than Q'.
'P © Q' means 'P is neither smaller than nor equal to Q'.
'P # Q' means 'P is neither smaller than nor equal to Q'.
'P % Q' means 'P' is not greater than Q'.
'P @ Q' means 'P is neither greater than nor smaller than Q'.

Now, in each of the following questions assuming the given statements to be true, find which of the four Conclusions I, II, III and IV given below them is/are definitely true and given your answer accordingly.

  1. Statements
    M @ B, B # N, N $ R, R © K
    Conclusions
    I. K # B
    II. R © B
    III. M $ R
    IV. N © M
    1. I and III are ture
    2. I and III are ture
    3. II and IV are ture
    4. II, III and IV are ture
    5. None of the above

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    Statements
    M @ B ⇒ M = B
    B # N ⇒ B > N
    N $ R ⇒ N ≥ R
    R © K ⇒ R < K
    i.e., M = B > N ≥ R < K
    Conclusions
    I. K # B ⇒ K > B          (x)
    II. R © B ⇒ R < B         (✔)
    III. M $ R ⇒ M ≥ R        (x)
    IV. N © M ⇒ N < M       (✔)
    Hence, II and IV are definitely true.

    Correct Option: C

    Statements
    M @ B ⇒ M = B
    B # N ⇒ B > N
    N $ R ⇒ N ≥ R
    R © K ⇒ R < K
    i.e., M = B > N ≥ R < K
    Conclusions
    I. K # B ⇒ K > B          (x)
    II. R © B ⇒ R < B         (✔)
    III. M $ R ⇒ M ≥ R        (x)
    IV. N © M ⇒ N < M      (✔)
    Hence, II and IV are definitely true.


  1. Statements
    F # H, H @ M, M © E, E $ J
    Conclusions
    I. J © M
    II. E # H
    III. M © F
    IV. F # E
    1. I and II are ture
    2. II and III are ture
    3. I, II and III are ture
    4. II, III and IV are ture
    5. None of the above

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    Statements
    F # H ⇒ F > H
    H @ M ⇒ H = M
    M © E ⇒ M < E
    E $ J ⇒ E ≥ J
    i.e., F > H = M < E ≥ J
    Conclusions
    I. J © M ⇒ J < M           (x)
    II. E # H ⇒ E > H          (✔)
    III. M © F ⇒ M < F        (✔)
    IV. F # E ⇒ F > E            (x)
    Hence, II and III are definitely true.

    Correct Option: B

    Statements
    F # H ⇒ F > H
    H @ M ⇒ H = M
    M © E ⇒ M < E
    E $ J ⇒ E ≥ J
    i.e., F > H = M < E ≥ J
    Conclusions
    I. J © M ⇒ J < M           (x)
    II. E # H ⇒ E > H          (✔)
    III. M © F ⇒ M < F        (✔)
    IV. F # E ⇒ F > E            (x)
    Hence, II and III are definitely true.



  1. Statements ::
    D % A, A @ B, B © K, K % M
    Conclusions ::
    I. B $ D
    II. K # A
    III. M # B
    IV. A © M
    1. I, II and IV are ture
    2. I, II and III are ture
    3. II, III and IV are ture
    4. I, III and IV are ture
    5. All are ture

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    Statements ::
    D % A ⇒ D ≤ A
    A @ B ⇒ A = B
    B © K ⇒ B < K
    K % M ⇒ K ≤ M
    i.e., D ≤ A = B < K ≤ M
    Conclusions
    I. B $ D ⇒ B ≥ D         (✔)
    II. K # A ⇒ K > A         (✔)
    III. M # B ⇒ M > B         (✔)
    IV. A © M ⇒ A < M         (✔)

    Correct Option: E

    Statements ::
    D % A ⇒ D ≤ A
    A @ B ⇒ A = B
    B © K ⇒ B < K
    K % M ⇒ K ≤ M
    i.e., D ≤ A = B < K ≤ M
    Conclusions
    I. B $ D ⇒ B ≥ D         (✔)
    II. K # A ⇒ K > A         (✔)
    III. M # B ⇒ M > B         (✔)
    IV. A © M ⇒ A < M         (✔)
    Hence, all Conclusion I, II, III and IV are definitely true.


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
    M @ D, D δ K, K © R
    Conclusions
    I. R $ M
    II. K δ M
    III. K $ M
    1. Only I is true
    2. Only II is true
    3. Only III is true
    4. Either II or III and I are true
    5. Either II or III is true

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    Statements
    M @ D ⇒ M ≥ K,
    D δ K ⇒ D = K, K © R ⇒ K > R
    So, M ≥ K = D > R
    Conclusions
    I. R $ M ⇒ R < M      (true)
    II. K δ M ⇒ K = M      ( may be)
    III. K $ M ⇒ K < M      ( may be)

    Correct Option: D

    Statements
    M @ D ⇒ M ≥ K,
    D δ K ⇒ D = K, K © R ⇒ K > R
    So, M ≥ K = D > R
    Conclusions
    I. R $ M ⇒ R < M      (true)
    II. K δ M ⇒ K = M      ( may be)
    III. K $ M ⇒ K < M      ( may be)
    So, from the given statements either II or III and I are true.



  1. Statements
    F ∗ T, T $ N, N @ R
    Conclusions
    I. R $ T
    II. N © F
    III. F $ R
    1. None is true
    2. Only I is true
    3. Only II is true
    4. Only III is true
    5. II and III are true

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

    Correct Option: C

    Statements
    F ∗ T ⇒ F ≤ T,
    T $ N ⇒ T < N, N @ R ⇒ N ≥ R
    So, F ≤ T < N ≥ R
    Conclusions
    I. R $ T ⇒ R < T      (false)
    II. N © F ⇒ N > F      (true)
    III. F $ R ⇒ F < R      (false)
    So, only Conclusion II is true from the given statements.