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Mathematical Operators

  1. Inequalities: Concept
     
    > Greater than
     
    < Less than
     
    ≥ Greater than or equal to
     
    ≤ Less than or equal to
     
    = equal to
  2. Combining Inequalities
     
    If A > B and B > C then we can say  → Combined form
     
    If A ≥ B and B ≥ C
     
    Then we can say   Combined form
  3. Order of Preference
     
    The preference order is: (1) >, < (2) ≥, ≤
     
    i.e. If A > B ≥ C, then A > C, ∴ while moving from A to C, we encounter ‘>’ sign and ‘≥’ sign the preference is to be given to the ‘>’ sign similarly, If ‘<’ and ‘≤’ sign appear together, then preference will be given to the ‘<’ sign.
     
    So, if A < B ≤ C, then A < C
     
    Solved Example:
     
    Relationship between A & C
    1. A ≥ B > C A > C
    2. A ≤ B ≤ C A ≤ C
    3. A < B ≤ C A < C
    4. A > B ≥ C A > C
    5. A ≥ B ≥ C A ≥ C
    6. If the direction of sign changes, then no relationship can be established.
       
      If X > Y ≥ Z ≥ Q, then we can safely say X > Z, X > Q and Y ≥ Q, ∵ the signs are in the same direction i.e. >, ≥, ≥.
       
      However, if X < Y > Z, then no relationship can be inferred between X and Z, as the direction of the signs is opposite i.e. <, >
       
      Similarly if X > Y ≤ Z ≥ P > Q
       
      Then Between
       
      X and Z no relation (>, ≤)
       
      X and P  no relation (>, <, ≥)
       
      Y and P  no relation (≤, ≥)
       
      Z and Q  Z > Q (≥, >)
  4. ‘Either or’ case
     
    If X ≥ Y, then the conclusions:
     
    (a) X > Y is false (∵ X ≥ Y, not X > Y) and
     
    (b) X = Y is false (∵ X ≥ Y, not X = Y)
     
    However,
     
    Either (a) or (b) is definitely true; either X > Y or X = Y, it is just like saying X ≥ Y.




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