ప్రకటన సరళీకృత చేయవచ్చు

ప్రకటన సరళీకృత చేయవచ్చు

CODED - INEQUALITIES

This is one of the easiest and most scoring topics in the bank examinations, either Probationary officers or clerks. A statement (expression) consists of a group of elements and the relationship among them, which would not be equal, may be given in coded form.

Before discussing on the steps to be followed for solving the questions, the meaning of certain symbols as well as some specific statements have to be clearly understood.

Symbols:  >, ³, <, £, ¹
·    The symbol '>' indicates greater than
·    The symbol '³' indicates greater than or equal to
·    The symbol '<' indicates lesser than
·    The symbol '£' indicates lesser than or equal to
·    The symbol '¹' indicates not equal to. The meaning of it is that either greater than or smaller than

Statements:
Statement 1: "A is not greater than B".
Explanation: If A is not greater than B means A should be either equal to B or lesser than B. So, It can be understood as A £ B
Statement 2: "A is not lesser than B".
Explanation: If A is not lesser than B, then A should be either equal to B or greater than B. It can be represented as A³B
Statement 3: "A is neither greater than nor equal to B".
Explanation: Based on the statement it is clear that A < B
Statement 4: "A is neither lesser than nor equal to B".
Explanation: If A is not either lesser than or equal to B then it should be greater than B which can be represented as A > B.
Statement 5: "A is neither greater than nor lesser than B".
Explanation: As A cannot be either greater than or lesser than B then A is equal to B.



Based on the above narration it is understood that the relationship among the elements may not be equal.
    So, the following steps have to be performed to derive the valid conclusions from the given statement/s.
1.    Firstly, the statement may be having different pairs of elements with a distinct relationship among them. These pairs of elements have to be properly arranged by identifying the connecting elements.
2.    The codes have to be understood and represented with the proper symbols in the statement.
3.    Checking the validity of conclusions based on the interpretation of the statement.

The following illustration helps in better understanding the subject
Example:
·    'P©Q' means 'P' is greater than 'Q'.
·    'P%Q' means 'P' is smaller than 'Q'.
·    'P@Q' means 'P' is either greater than or equal 'Q'.
·    'P$Q' means 'P' is either smaller than or equal to 'Q'.
·    'P#Q' means 'P' is equal to 'Q'.
Statement:
C © D, A % B, E @ F, D $ E, B # C
Step 1:
©  ®  >
%  ®  <
@  ®  ³
$   ®   £
#    ®  =
A%B, B#C, C©D, D$E, E@F, (B is a connecting element for the pairs AB and BC. C is a connecting element for BC and CD. D is a connecting element for CD and DE, and E for the pairs DE and EF).
    So, the statement can be simplified as A% B # C © D $ E @ F
Step 2:
The meaning of the complete statement A% B#C©D$E@F is
    A <  B = C > D £ E ³ F
Step 3:
1.    B > D
2.    A < C
Both the conclusion 1 and 2 are true.

Questions:
In each of the following questions, assuming the given statements to be true, find out which of the two conclusions I and II given below them is/are definitely true. Give answer
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 conclusions I and II are true.

Directions (Q 1-10):
In the following questions, the symbols $,@,%, © and # are used with the following meanings as illustrated below:
·    'P©Q' means 'P' is greater than 'Q'.
·    'P%Q' means 'P' is smaller than 'Q'.
·    'P@Q' means 'P' is either greater than or equal 'Q'.
·    'P$Q' means 'P' is either smaller than or equal to 'Q'.
·    'P#Q' means 'P' is equal to 'Q'.
1)    Statements: M @ R, R ©F, F#L
    Conclusions: I. R@L     
                    II.M@L
    Solution: 4.
    M ³ R>F=L. So, R>L. Hence, conclusion I is not true. Even, the Conclusion II is not true.
2)    Statements: T $ J, J @ V, V # W
    Conclusions: I. T©W    II. W@T
    Solution: 3
    T £ J ³ V= W
    Either I or II follows.
3)    Statements: J @ D, D$ L, L#N
    Conclusions: I. J # L     
                    II. J $ L
    Solution: 4
    J  ³ D £ L = N
    Both the conclusions are not true
4)    Statements: R $ M, M%H,H$F
    Conclusions: I. R % F     
                    II. M$F
    Solution: 1
    R £ M < H £ F.
    Hence, R< F. Conclusion I is true. As M< F conclusion II is not true.
5)    Statements: K $ H, H % I, I © F
    Conclusions: I. K $ I  
                          II.H % F
    Solution: 4
    K £ H < I > F.
    As K< I, conclusion I is not true. H and F can't be compared. Hence, conclusion II is not true.
6)    Statements: K @ B, B#J, J ©T
    Conclusions: I. K#T     
                    II. B@T
    Solution: 4
    K ³ B = J >T
    K > T. Hence, Conclusion I is not true. B >T. So, conclusion II is not true.
7)    Statements: F $ M, M @L,L#W
    Conclusions: I. W$M    II. F@L
    Solution: I
    F £ M ³ L = W
    M ³ W. By conversion W £ M. Hence, conclusion I is true. We can't compare F and L. Hence, conclusion II is not true.
8)    Statements: R #Q, Q @F, F % A
    Conclusions: I. R ©A   II. R#F
    Solution: 4
    R = Q ³ F < A
    We can't compare R and A. Hence, conclusion I is not true. R ³ F. Hence, conclusion II is not true.
9)    Statements: V$X, X © Y, Y % H
    Conclusions: I. Y@V  II. H#V
    Solution: 4
    V £ X > Y < H
    We can't compare V and Y. Hence, conclusion I is not true. Again, H and V can't be compared. So, conclusion II is not true.
10)    Statements: M@ B,B # A,A @F
    Conclusions: I. M #A    II. B#F
    Solution: 4
    M ³ B = A ³F
    As M ³ A, conclusion I is not true. Again, as B³F, conclusion II is not true.