I have already explained this topic in previous post of Reasoning Coded Inequalities Topic Explanation. Now I found this in more simplified way to explain this Coded Inequalities Topic with sample question examples explanation I'm sharing it with you. 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 the coded form.

We know that when 2 is multiplied by 2 we get 4 (2 × 2 = 4). This is a case of equality.

But, we know that when 1 is multiplied by 2 we get 2(1 × 2 = 2).

This means that 1 × 2 is not equal to 4 (1 × 2 ≠ 4) as 4 is greater than 2.

In the same way when 2 is multiplied by 4 we get 8 (2 × 4 = 8)

Hence, this means that 2 × 4 ≠ 4 as 4 is lesser than 8. These are the cases of Inequality.

So, the relationship between the elements has to be clearly understood.

Firstly, let us focus on the following before solving the questions.

List of the signs and their meaning.

Understanding the terms

Organising the statements in the given question

How to draw conclusions.

Signs: >, >, <, <, ≠

The sign '>' indicates greater than

The sign '>' indicates either greater than or equal to

The sign '<' indicates lesser than

The sign '<' indicates either lesser than or equal to

The sign '≠' indicates not equal to. The meaning of it is that either greater than or smaller than

The Element near to the open end is greater than the one which is nearer to the closed end.

For Example, in the expression A>B, A is greater than B or B is lesser than A (B<A).

For Example,In the expression C<D, C is lesser than D or D is greater than C(D>C).

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

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 A>B

Explanation: Based on the statement it is clear that A<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.

Explanation: As A cannot be either greater than or lesser than B then A is equal to B (A=B).

If A>B, then it is B<A

If A<B, then it is B>A

If A>B, then it is B<A

If A<B, then it is B>A

Organising and understanding the statements in the given question

The statement may be having different pairs of elements with a distinct relationship among them. It is to be seen whether these pairs of elements can be properly arranged to make a chain by identifying the common elements.

Here, B is a common element. So, the two expressions can be connected and understood as A>B>C

The following table is highly helpful to the students in order to know the valid conclusion/s for various statements given below.

As it may be noticed above, when the signs are in the same direction (>>, > ≥, ≥>, >= ) between the elements in the statement, then the element nearer to the open end (A)is greater than the one which is nearer to the closed end(C).

Even here it is noticed that when the signs are in the same direction (<<, <≤, ≤< ) between the elements in the statement, the element nearer to the closed end (A)is lesser than the one which is nearer to the open end(C) or C is greater than A.

When the signs ≥,= are there between the elements in the statement, then "≥" must be preferred.

When the signs ≤,= are there between the elements in the statement, then "≤"must be preferred.

When the signs are in the opposite direction (>< or >≤ or≥ < etc) between the elements (A&C) in the statement, then we can't determine the relation between them. Hence, those elements (A&C) form a complementary pair.

Generally, relationship between the elements in the given statements is coded.

1. Firstly, the elements in the statement have to be connected to make a chain.

2. Now, the codes are to be represented by the proper symbols in the statement (chain).

3. Check 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 to 'Q'.

'P$Q' means 'P' is either smaller than or equal to 'Q'.

'P#Q' means 'P' is equal to 'Q'.

Question:

Statement: C©D, A%B, E@F, D$E, B#C

Conclusions:

1. B>D 2. A<C

A%B, B#C C©D D$E E@F (B is a common element for the pairs AB and BC. C is a common element for BC and CD. D is a common element for CD and DE, and E for the pairs of DE and EF).

So, the statement can be simplified as A % B # C © D $ E @ F

© → >

% → <

@ → ≥

$ → ≤

# → =

The relation between the elements of the complete statement is

A % B # C © D $ E @ F → A < B = C > D ≤ E ≥ F

1. B > D

2. A < C

Conclusion B > D is true as B=C>D.

Conclusion A < C is also true as A< B=C.

Hence, both the conclusions I and 2 are true.

The Explanation given below for each of the following questions will give complete clarity on the subject.

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.

'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

Explanation and Solution:

M ≥ R>F=L. (R is a common element for the pairs M R and RF. F is a common element for RF and FL)

R © L → R>L. Hence, conclusion I is true.

M © L → M>L. Hence, conclusion II is also true.

2) Statements: T $ J, J @ V, V # W

Conclusions: I. T©W II. T $W

Explanation and Solution:

T ≤ J ≥ V= W ( J is a common element for the pairs TJ and JV. V is a common element for JV and VW).

The conclusions T > W and T ≤ W form a complementary pair (opposite signs between T & W) . Hence, Either I or II follows.

3) Statements: R $ M, M%H, H$F

Conclusions: I. R %F II. M $ F

Explanation and Solution: 1

R ≤ M<H ≤ F.

Hence, R< F. Conclusion I is true. As M< F, conclusion II is not true.

4) Statements: F $ M, M @L, L#W

Conclusions: I. F $ W II. F©L

Explanation and Solution: 3

F ≤ M ≥ L=W

The conclusions F ≤ W and F > L ( L = W) form a complementary pair. Hence, Either I or II follows.

**What is Inequality?**We know that when 2 is multiplied by 2 we get 4 (2 × 2 = 4). This is a case of equality.

But, we know that when 1 is multiplied by 2 we get 2(1 × 2 = 2).

This means that 1 × 2 is not equal to 4 (1 × 2 ≠ 4) as 4 is greater than 2.

In the same way when 2 is multiplied by 4 we get 8 (2 × 4 = 8)

Hence, this means that 2 × 4 ≠ 4 as 4 is lesser than 8. These are the cases of Inequality.

So, the relationship between the elements has to be clearly understood.

Firstly, let us focus on the following before solving the questions.

List of the signs and their meaning.

Understanding the terms

Organising the statements in the given question

How to draw conclusions.

Signs: >, >, <, <, ≠

The sign '>' indicates greater than

The sign '>' indicates either greater than or equal to

The sign '<' indicates lesser than

The sign '<' indicates either lesser than or equal to

The sign '≠' indicates not equal to. The meaning of it is that either greater than or smaller than

**The following help us in understanding the sign:**The Element near to the open end is greater than the one which is nearer to the closed end.

**Open end → > ← Closed end**

**Closed end → < ← Open end**

**Terms:****Term1. "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

**Term 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 A>B

**Term 3: "A is neither greater than nor equal to B".**Explanation: Based on the statement it is clear that A<B

**Term 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.

**Term 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 (A=B).

**First Technique Tip:**If A>B, then it is B<A

If A<B, then it is B>A

If A>B, then it is B<A

If A<B, then it is B>A

Organising and understanding the statements in the given question

The statement may be having different pairs of elements with a distinct relationship among them. It is to be seen whether these pairs of elements can be properly arranged to make a chain by identifying the common elements.

**Example 1:**A>B, B>C .Here, B is a common element. So, the two expressions can be connected and understood as A>B>C

**Example 2:**A>B, B>C. It can be understood as A>B>C (B is a common element)**Example 3:**A>B, B=C. It can be understood as A>B=C (B is a common element)**How to draw conclusions:**The following table is highly helpful to the students in order to know the valid conclusion/s for various statements given below.

**Second Technique Tip:**As it may be noticed above, when the signs are in the same direction (>>, > ≥, ≥>, >= ) between the elements in the statement, then the element nearer to the open end (A)is greater than the one which is nearer to the closed end(C).

**Third Technique Tip:**Even here it is noticed that when the signs are in the same direction (<<, <≤, ≤< ) between the elements in the statement, the element nearer to the closed end (A)is lesser than the one which is nearer to the open end(C) or C is greater than A.

**Fourth Technique Tip:**When the signs ≥,= are there between the elements in the statement, then "≥" must be preferred.

**Fifth Technique Tip:**When the signs ≤,= are there between the elements in the statement, then "≤"must be preferred.

**Sixth Technique Tip:**When the signs are in the opposite direction (>< or >≤ or≥ < etc) between the elements (A&C) in the statement, then we can't determine the relation between them. Hence, those elements (A&C) form a complementary pair.

Generally, relationship between the elements in the given statements is coded.

1. Firstly, the elements in the statement have to be connected to make a chain.

2. Now, the codes are to be represented by the proper symbols in the statement (chain).

3. Check 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 to 'Q'.

'P$Q' means 'P' is either smaller than or equal to 'Q'.

'P#Q' means 'P' is equal to 'Q'.

Question:

Statement: C©D, A%B, E@F, D$E, B#C

Conclusions:

1. B>D 2. A<C

**Step 1:**A%B, B#C C©D D$E E@F (B is a common element for the pairs AB and BC. C is a common element for BC and CD. D is a common element for CD and DE, and E for the pairs of DE and EF).

So, the statement can be simplified as A % B # C © D $ E @ F

**Step 2:**© → >

% → <

@ → ≥

$ → ≤

# → =

The relation between the elements of the complete statement is

A % B # C © D $ E @ F → A < B = C > D ≤ E ≥ F

**Step3:**Conclusions:1. B > D

2. A < C

Conclusion B > D is true as B=C>D.

Conclusion A < C is also true as A< B=C.

Hence, both the conclusions I and 2 are true.

The Explanation given below for each of the following questions will give complete clarity on the subject.

**Practice 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 (1-4): 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

Explanation and Solution:

M ≥ R>F=L. (R is a common element for the pairs M R and RF. F is a common element for RF and FL)

R © L → R>L. Hence, conclusion I is true.

M © L → M>L. Hence, conclusion II is also true.

2) Statements: T $ J, J @ V, V # W

Conclusions: I. T©W II. T $W

Explanation and Solution:

T ≤ J ≥ V= W ( J is a common element for the pairs TJ and JV. V is a common element for JV and VW).

The conclusions T > W and T ≤ W form a complementary pair (opposite signs between T & W) . Hence, Either I or II follows.

3) Statements: R $ M, M%H, H$F

Conclusions: I. R %F II. M $ F

Explanation and Solution: 1

R ≤ M<H ≤ F.

Hence, R< F. Conclusion I is true. As M< F, conclusion II is not true.

4) Statements: F $ M, M @L, L#W

Conclusions: I. F $ W II. F©L

Explanation and Solution: 3

F ≤ M ≥ L=W

The conclusions F ≤ W and F > L ( L = W) form a complementary pair. Hence, Either I or II follows.

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