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Reasoning inequality has been an important part of all public examinations in India. Over the years, competition has increased significantly. This calls for a better understanding of all related concepts. Reasoning inequality can be defined as expressions that consist of inequality signs, including <, >, =, and so on.
In order to get a deeper understanding of the concept of mathematical equalities, aspirants are supposed to have a brief idea about most signs which are used in maths or while solving mathematical problems.
Concept of Reasoning Inequalities
Reasoning inequality is a set of elements with a number of coded relationships mentioned as <, >, = ≤ or ≥. The inequality symbols are as follows:
1. Less than (<)
2. Greater than (>)
3. Less than or equal (≤)
4. More than or same as (≥)
5. Not equal symbol (≠).
Sample Questions for Inequality
Let’s assume the statement is P < S < R < T > Q
Q1. Based on the statement given above, which of these given conclusions is incorrect?
P < R
S < T
No relation between P & T
No relation between P & Q
P < T
The correct answer is option 4.
Reasoning Inequality–Symbol & Inference
Symbol | Inference |
X > Y | X is greater than Y |
X < Y | X is less than Y |
X = Y | X is neither equal to nor greater than Y |
X ≤ Y | X is equal to or smaller than Y |
X ≥ Y | X is equal to or greater than Y |
Types of Inequalities in Logical Reasoning for Competitive Exams
Basic Inequalities: This covers expressions that consist of a quick comparison among all the elements.
Either-Or: It is not possible to determine the definite relationship between any two elements. Here, only two relations will be mentioned, of which either 1 or 2 can be right.
Coded Inequalities: Codes are assigned to the inequality symbols, and the expressions are given using these codes. Candidates are supposed to decode the symbols and hunt for the relationship between all given elements.
Signs used to denote Inequality | 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 | ‘>’ shows more than or same as, which means, a is more than b or same as b |
Strict Inequalities | |
If a < b, then | ‘<’ denotes less than, that is, a is less than b |
If a > b, then | ‘>’ shows greater than. It means a here is more than b |
Properties of Inequalities in Logical Reasoning
Property | ≥ | ≤ |
Multiplication | If a ≥ b, further ac ≥ bc, where c > 0 | If a ≤ b, further ac ≤ bc, where c > 0 |
Subtraction | If a ≥ b, further a – c ≥ b – c | If a ≤ b, further a – c ≤ b – c |
Addition | If a ≥ b, further a + c ≥ b + c | If a ≤ b, further a + c ≤ b + c |
Division | If a ≥ b, further a/c ≥ b/c, where c > 0 | If a ≤ b, further a/c ≤ b/c, where c > 0 |
Transitivity | If a ≥ b further b ≥ c then, a ≥ c | If a ≤ b and b ≤ c then, a ≤ c |
Multiplicative | If a ≥ b, further 1/a ≤ 1/b, in case a > 0, b > 0 | If a ≤ b, further 1/a ≥ 1/b, if a > 0, b > 0 |
Inverse Additive | If a ≥ b, further -a ≤ -b, in case >0, b > 0 | If a ≤ b, further -a ≥ -b, in case a>0, b > 0 |
Tips and Tricks to Solve Reasoning Inequality Questions
Here’s how you can attemple inequality-related problems:
Before you go for inequality-related problems, make sure you are well-versed with all the mathematical expressions along with their representation. A clear understanding of them is extremely important to answer questions well.
Candidates are required to use a short trick to find answers easily and faster. The priority of solving questions needs to be set on the basis of relationships used along with their seniority.
When you are solving the coded inequality questions, remember to make quick diagrams along with rough graphs while mentioning the codes. It minimises time wastage.
Solved Questions of Inequality –
Here is Statement: P < S < R < T > Q
Q1. Have a look at all given statements and decide which of these conclusions are not true.
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
Questions about inequality and coded inequality are mostly asked in all public examinations. A greater understanding of the concept is crucial since the competition level has increased over the years. Reasoning inequalities can be described as an expression that consists of inequality signs, which include <, >, =, and so on.
