REASONING ENEQUALITIES

                   INEQUALITIES

In this type, statements is given which have certain coded or decoded relationship is given among symbols, then we need to find out  conclusion relationship base upon that of statements.

    Rules to find inequalities:  

1.     Two inequalities can be combined if and only if they have a common term.

2.     Two inequalities can be combined if and only if the common term is greater than (or greater than or equal to) one and less than (or less than or equal to) the other.

Example:

a)      A>B ,  B>C

     Here “B” has common case in first term “B” is less and other term it is   greater. Therefore we can find some relationship i.e.  “A >B>C”     also

b)     A>B  ,C >D

     Here we do not have common case. So we cannot find the relationship.

c)     A>B  ,C >B

   Here in “B” is common terms, but in both case” is less than other term.

3.     The conclusion inequality will have a “≥” sign (or a “≤” sign) if and only if both the signs in the combined inequality were” ≥” or “≤”.

                       

Example:

a)      A>B ,  B>C

     Here “B” has common case in first term “B” is less and other term it is   greater. Therefore we can find some relationship i.e.  “A >B>C”     also “A>C”.

b)    A≥B ,  B≥C

     Here “B” has common case in first term “B” is less and other term it is   greater. Therefore we can find some relationship i.e.  “A ≥B≥C”     also “A≥ C”.

4.     Either 1  or 2  follows: if after the third step if you find following  conclusion ,then condition will follow.

a)     If you get conclusion   “A≥B” and given conclusion 1.“A>B”   and   2.“A=B”. then either 1 or 2 follow.

b)    If you do not get any conclusion then and  given conclusion  1. “≤”  and 2.  “>” . then either 1 or 2 follow.

c)     If you do not get any conclusion then and  given conclusion  1. “<”   and 2.  “≥” . then either 1 or 2 follow.

d)    If you do not get any conclusion then and  given conclusion  1. “>”   and 2.  “≤” . then either 1 or 2 follow.

e)     If you do not get any conclusion then and  given conclusion  1. “≥”   and 2.  “<” . then either 1 or 2 follow.

Direction : Given below some option choose best one according to the question

1.     If only conclusion   I is true.

2.     If only conclusion   II is true.

3.     If either I or II  is true.

4.     If neither I nor II  is true.

5.     If both I and  II  is true.

       Example 1:  Given statements

                                A≥ B, B=D, D ≤C, C≤ B

Conclusion:

                                        I.            A≥B

                                      II.            A

Solution :

                                        I.            By looking  given conclusion is true in the statements.

                                      II.            Here we have to find relationship between A and C . now thus choose all possible way for getting relationship .

   i.e.       A≥B≥C

         Thus       A≥C

                        thus this  conclusion  is not true.

     Thus option 1)  is correct.

 Example 2:  Given statements

                                A≥ B, B=D, D ≤C, C ≥B

Conclusion:

                                        I.            A≥C

                                      II.            A

Solution:

       

                                                    I.               Here we have to find relationship  A  and C ,here we have common term B ,which is lesser in both terms. Thus we are unable to find the relationship among them.

                                                  II.                Since we are unable to find relationship.

                           Thus If either I or II  is true.  Then option 3) are correct.

Direction : In the following question, the different symbols  are used with the following meaning.

 P α  Q  means P is greater than Q.

 P β  Q  means P either greater than or equal to  Q.

 P γ Q  means P equal to Q.

P δ Q  means P smaller than Q.

P η Q  means P either smaller than or equal to Q.

       

      And   option to choose is

1.     If only conclusion   I is true.

2.     If only conclusion   II is true.

3.     If either I or II  is true.

4.     If neither I nor II  is true.

5.     If both I and  II  is true.

Example 2:  Given statements

                                 M β I, T γ B, M δ A, I α T

Conclusion:

                                        I.            M γ T

                                      II.            A α I

Solution:

         Since relationship is in coded form so we have to decode at first.

  Now

   .    α  means   >(greater than)

        β  means     ≥   (greater than or equal)

        γ  means   =  (equal)

        δ  means  <  (smaller)

       η  means   ≤  (smaller than or equal)

this decode the  statements

                M ≥   I,  T  =   B,  M < A,  I > T

   And  conclusions

                                        I.             M =  T

                                      II.            A > I

                 Now we have find the truthiness of these conclusion

                                        I.             Here we have to find relationship between M and T .

          Now   M≥I>T

             Thus  M>T

               Therefore this option is not correct.

                     

                                      II.            A > I

        Here we have to find relationship between A and I.

          Now  A>M≥I

             Thus  A>I

               Therefore this option is correct.

    Now  option 2)  is correct.