basic of inequality in reasoning
Answers
Explanation:
Inequality is a phenomenon that we have known or come across for a while now. It simply means something that is not equal in all the sense whether social, economical or mathematical sense. But today we are talking about Inequalities in mathematical terms. Each one of you has seen signs such as “>”, “≠”, “≤” etc. at some point of time or other. And all those who had math’s in their high school are thoroughly acquainted with the concept and comfortable in solving problems of Inequalities. So, for all those who have little or no idea about them, I will give you a brief introduction about this concept that will be sufficient to solve problems which is the essence of the discussion of this article.
Signs used to denoteInequalityMeaningIf a ≠ b, then≠ denotes not equal to, i.e. a is not equal to bIf a ≤ b, then‘≤’ denotes less than or equal to, i.e. a is less than b or at most bIf a ≥ b, then‘>’ denotes greater than or equal to, i.e. a is greater than b or at least bStrict InequalitiesIf a <b, then‘<’ denotes less than, i.e. a is less than bIf a > b, then‘>’ denotes greater than, i.e. a is greater than b
Properties of Inequalities
Property≥≤AdditionIf a ≥ b, then a + c ≥ b + cIf a ≤ b, then a + c ≤ b + cSubtractionIf a ≥ b, then a – c ≥ b – cIf a ≤ b, then a – c ≤ b – cMultiplicationIf a ≥ b, then ac ≥ bc, where c>0If a ≤ b, then ac ≤ bc, where c>0DivisionIf a ≥ b, then a/c ≥ b/c, where c>0If a ≤ b, then a/c ≤ b/c, where c>0TransitivityIf a ≥ b and b ≥ c then, a ≥ cIf a ≤ b and b ≤ c then, a ≤ cInverse. Additive,If a ≥ b, then -a ≤ -b, if a>0, b>0If a ≤ b, then -a ≥ -b, if a>0, b>0 ·MultiplicativeIf a ≥ b, then 1/a ≤ 1/b, if a>0, b>0If a ≤ b, then 1/a ≥ 1/b, if a>0, b>0
The above-mentioned properties also hold for strict inequalities.
Now let’s move forward to our topic of interest. Consider the following question,
A α B means A is greater than B
A β B means A is either greater than or equal to B
A γ B means A is equal to B
A δ B means A is small than B.
A η B means A is either smaller than or equal to B
Now on the basis of the statement given below be true, find which of the following conclusion holds to be true?
Statement: E γ F, C δ D, F β G, D α E
Conclusion 1: E α G
Conclusion 2: C γ E
If only conclusion 1 holdsIf only conclusion 2 holdsIf either 1 or 2 is trueIf neither 1 nor 2 is trueIf both 1 and 2 are true.
If you carefully examine the above question you can find out that symbols are used to represent various inequalities and with the support of these inequalities conclusions are framed which defines a relationship between two variable and you have to judge whether these relationships are true or False. In summary, you have to decode the above coded inequalities and determine their validity. These kinds of questions come in various competitive exams such as Bank PO, SSC, CAT etc. These questions can prove to be effortless and simple to solve if you now the right technique and methods to do so otherwise, they can be perplexing and time-consuming. In this blog, I will provide you straightforward and direct methods and steps on how to approach these types of problems and solve them rapidly.