Mathematical operation and symbol notation


  1. In which of the following expressions does the expression 'M' > R' does not hold true ?
    1. M = P > Q > R
    2. M > P ≥ Q = R
    3. R = P < Q < M
    4. R , Q ≤ P = M
    5. M = P < Q = R

  1. View Hint View Answer Discuss in Forum

    We can check all the options one by one.
    from option (a),
    M = P > Q > R ⇒ M > R
    So, expression M > R holds true for option (a).
    From option (b),
    M > P ≥ Q = R ⇒ M > R
    So, expression M > R holds true for option (b).
    From option (c).
    R = P < Q < M ⇒ R < M
    So, expression M > R holds true for option (c).
    From option (d),
    R < Q ≤ P = M ⇒ R < M
    So, expression M > R holds true for option (d)
    From option (e),
    M = P < Q = R ⇒ M < R

    Correct Option: E

    We can check all the options one by one.
    from option (a),
    M = P > Q > R ⇒ M > R
    So, expression M > R holds true for option (a).
    From option (b),
    M > P ≥ Q = R ⇒ M > R
    So, expression M > R holds true for option (b).
    From option (c).
    R = P < Q < M ⇒ R < M
    So, expression M > R holds true for option (c).
    From option (d),
    R < Q ≤ P = M ⇒ R < M
    So, expression M > R holds true for option (d)
    From option (e),
    M = P < Q = R ⇒ M < R
    So, expression M > R does not hold true for option (e).


  1. Statements
    H ≥ I = J > K ≤ L
    Conclusions
    I. K < H
    II. L ≥ I
    1. If only Conclusions I is true
    2. if only Conclusions II is true
    3. if either Conclusions I or II is true
    4. if neither Conclusions I nor II is true
    5. if both Conclusions I and II are true

  1. View Hint View Answer Discuss in Forum

    Given that,
    H ≥ I = J > K ≤ L
    Here, statements are already combined
    H ? I = J > K means H > K
    Conclusions
    I. K < H     (true)
    II. L ≥ I     (false)

    Correct Option: A

    Given that,
    H ≥ I = J > K ≤ L
    Here, statements are already combined
    H ? I = J > K means H > K
    Conclusions
    I. K < H     (true)
    II. L ≥ I     (false)
    So, it is clear that only Conclusion I follows from the given statements.



  1. Statements
    S > C ≥ 0, P < C
    Conclusions
    I. 0 < P
    II. S > P
    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

    Given that
    S > C ≥ O ....(i)
    P < C ...............(ii)
    On combined the statement (i) and (ii), we get
    S > C > P
    P < C ≥ O
    Conclusions
    I. O < P............... (false)
    II. S > P ................ (true)

    Correct Option: A

    Given that
    S > C ≥ O ....(i)
    P < C ...............(ii)
    On combined the statement (i) and (ii), we get
    S > C > P
    P < C ≥ O
    Conclusions
    I. O < P............... (false)
    II. S > P ................ (true)
    So, it is clear that only Conclusion II follow from the given statements.


  1. Statements
    A = B ≤ C,
    A > R
    Conclusions
    I. B > R
    II. R < C
    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

    Given that,
    A = B ≤ C ................(i)
    A > R .........................(II)
    On combining the statements (i) and (ii), we get
    R < A = B ≤ C
    Conclusion
    I. B > R. .................(true)
    II. R < C .................(true)

    Correct Option: E

    Given that,
    A = B ≤ C ................(i)
    A > R .........................(II)
    On combining the statements (i) and (ii), we get
    R < A = B ≤ C
    Conclusion
    I. B > R. .................(true)
    II. R < C .................(true)
    So, it is clear that both Conclusions I and II follow from the given statements.



  1. Statements
    D > E ≤ F,
    J < F
    Conclusions
    I. D > J
    II. E < J
    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

    Given that,
    D > E ≤ F ..............(i)
    J < F .........................(ii)
    On combining the statements (i) and (ii), we get
    D > E ≤ F > j
    Conclusions
    I. D > J
    II. E < J

    Correct Option: D

    Given that,
    D > E ≤ F ..............(i)
    J < F .........................(ii)
    On combining the statements (i) and (ii), we get
    D > E ≤ F > j
    Conclusions
    I. D > J       (false)
    II. E < J       (false)
    So, it is clear that neither Conclusion I nor II is true .