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Questions about inequality and coded inequality are mostly an integral part of all public examinations. Over the years, the competition level in public examinations has increased considerably. Hence, a greater understanding of the concept is crucial.
Before understanding the concept of coded inequality, it is important to know the concept of inequality. In mathematics, equality is defined as a relationship between two numbers or expressions of greater than, greater than or equal to, less than, or less than or equal to. Inequalities are used to compare numbers. The inequality symbols are:
- Less than (<)
- Greater than (>)
- Less than or equal (≤)
- Greater than or equal (≥)
- Not equal symbol (≠).
To better understand the concept behind mathematical equalities, candidates should possess a greater understanding of all signs used in mathematics while solving problems. Inequalities can be classified into three major types:
- Basic inequalities
- Either or case
- Coded-inequalities
Inequality Signs | Meaning |
If a ≠ b, then | ≠ denotes not equal to, that is, a is not equal to b |
If a ≤ b, then | ‘≤’ denotes less than or equal to, that is, a is less than b or at most b |
If a ≥ b, then | ‘>’ denotes greater than or equal to, that is, a is greater than b or at least b |
Strict Inequalities | |
If a <b, then | ‘<’ denotes less than, that is, a is less than b |
If a > b, then | ‘>’ denotes greater than, that is, a is greater than b |
Inequality in Logical Reasoning
Reasoning inequality can be described as an expression that consists of inequality signs or an expression with a series of elements with several coded relationships expressed as <, >, = ≤ or ≥, and so on.
Reasoning Inequality: Symbol and Inference | |
Symbol | Inference |
X > Y | X is greater than Y |
X < Y | X is less than Y |
X = Y | X is neither equal nor greater than to Y |
X ≤ Y | X is equal or smaller than Y |
X ≥ Y | X is equal or greater to Y |
Properties of Inequalities
Property | ≥ | ≤ |
Addition | If a ≥ b, then a + c ≥ b + c | If a ≤ b, then a + c ≤ b + c |
Subtraction | If a ≥ b, then a – c ≥ b – c | If a ≤ b, then a – c ≤ b – c |
Multiplication | If a ≥ b, then ac ≥ bc, where c>0 | If a ≤ b, then ac ≤ bc, where c>0 |
Division | If a ≥ b, then a/c ≥ b/c, where c>0 | If a ≤ b, then a/c ≤ b/c, where c>0 |
Transitivity | If a ≥ b and b ≥ c, then a ≥ c | If a ≤ b and b ≤ c, then a ≤ c |
Inverse Additive | If a ≥ b, then -a ≤ -b, if a>0, b>0 | If a ≤ b, then -a ≥ -b, if a>0, b>0 |
Multiplicative | If a ≥ b, then 1/a ≤ 1/b, if a>0, b>0 | If a ≤ b, then 1/a ≥ 1/b, if a>0, b>0 |
Types of Inequalities
Here is the detailed information about the types of inequalities –
- Basic inequalities: In basic inequalities, expressions that consist of a quick comparison between all elements will be provided and the relationship between the two will be asked to determine.
- Either or case: In either or case type of inequality, it is impossible to determine the definite relationship between any two elements. Here, only two relations will be mentioned. Out of these two, either 1 or 2 can be correct.
- Coded-inequalities: Coded inequalities are the third type of inequalities where codes are assigned to the inequality symbols. Also, the expressions are given using these codes. Candidates are supposed to decode the given symbols and hunt the relationship between all given elements.
Coded-Inequality
In questions on coded-inequality, symbols are given that represent different types of inequalities. With the help of these inequalities, a relationship between two variables has to be established, and a conclusion reached. On the basis of this information, the candidate has to decide or decode whether the relationship between the variables is true or false.
How do we solve Inequality-Related Problems?
There are various tricks to solve inequality-related problems:
- Aspirants should consider symbols using a trick for finding the answers quickly. The priority to solve the problems should be set based upon the relations used and their seniority.
- Before attempting any inequality-related question, be prepared with all mathematical signs along with their representation. Once you have a clear idea of it, you will be able to find the correct answer.
- While attempting the question for coded inequality, make sure you draw a diagram or a rough graph which mentions what all codes represent. It will prevent any wastage of time.
Solved Question of Inequality –
Here is the Statement: P < S < R < T > Q
Q1. Based on the given statement, which of these given conclusions is not right?
- P < R
- S < T
- No relation between P & T
- No relation between P & Q
- P < T
The correct answer is option D) No relation between P & Q
Conclusion
Reasoning inequalities is classified into three major types: coded inequalities, either/or, and basic inequalities. Coded inequalities is a type of inequalities where codes are assigned to the inequality symbols. Also, the expressions are given using these codes. Candidates are supposed to decode the given symbols and hunt the relationship between all given elements.
In order to solve reasoning questions successfully, it is important to read and understand the information carefully, analyse it intricately, think of all potential solutions, compare all answers obtained from all possibilities and then reach the right logical conclusion.
