Direct Inequalities “Either Or” Cases

Part III

Introduction:-

This article is a continuation of my previous article regarding Direct Inequalities and this article mainly based on the Either Or case & complementary pairs in direct inequalities problems. I’m going to explain you how to solve this inequalities problem within a minute by using the same method that we saw in our previous article.

Either or cases are otherwise called as complementary pairs. Here we have two types of cases they are as follows:

• Relational
• Non Relational

Relational Cases:-

If we have only open gate in between the source and destination entities in the statement then that conclusion falls under relational case

We can combine two elements with common elements in which two relations are established.

Important Rules:

There are three condition that should satisfy to qualify for Non Relational Either Or case. The three conditions are as follows:

• The subject and predicate should be same i.e. the either or will only qualify if the conclusion is between two same subjects and predicates only.
• Both the individual conclusion must be false.
• If we have Greater than or equal to ≥ and Lesser than or equal to ≤ relationship between the entities, Two possibilities > and = or < and = must be discussed in the conclusion.

Let us take an example through which we can understand the questions step by step.

Eg:- Statement : A≥B≥C>D<E

Conclusion : I. A > C           II. A= C

We have only open gate between A and C. Then we have two relation between them ‘≥”. But In such cases we can club these two symbols ‘>’ and ‘=’ to make our conclusion satisfy the statement. The above conclusions are the case of Either Or.

Eg:- Statements: A ≤ B ≤ C ≤ D < E

Conclusions: I. A < D           II. A = D

Conclusion doesn’t form the complementary pairs but still here the answer is either-or because only two relations can be established between A and C. Here conclusion either I or II follows, because here we can say A is either greater than C or equal to C.

Non Relational Cases:- 

In the given statement,  If we have closed gate between the source and destination entities. Then, it falls under the Non Relational case.

We cannot combine two elements with common elements in which no relation is established.

Important Rules:

There are three condition that should satisfy to qualify for Non Relational Either Or case. The three conditions are as follows:

• The subject and predicate should be same i.e. the either or will only qualify if the conclusion is between two same subjects and predicates only.
• Both the individual conclusion must be false.
• Both the subject should have all the three possibility i.e. >, <, =.

There can be only three possibilities between two subjects i.e.

i. A>B

ii. A=B

iii. A<B

Let us take an example through which we can understand the questions step by step.

Eg:-       Statement : A>B<C<D

Conclusion: I. A≥C             II. A<C

In the above example, there is a closed gate between A and G. So, it falls under Non Relational case, and these conclusions follow the three conditions that we mentioned above. Therefore these two conclusions are the case of Either I nor II are true.

Eg:-       Statement : A>B=C≥D>E≥F≤G<H

Conclusion : I. A>G            II. A<G

In the above example, there is a closed gate between A and G. So, it falls under Non Relational case and also we cannot determine whether A is greater than G or A is smaller than G. These two conclusions doesn’t satisfies the third condition. Therefore this is the case of Neither I nor II are true.

Eg:-        Statement : A>B=C≥D>E≥F≤G<H

Conclusion : A>G A≤G

If you look at the previous example both are quite similar to each other. but the only difference is it  satisfying the third condition as well, Therefore this is the case of Either I or II is True.

Problems for Practice:

1.Statement : A=B≤C>D

Conclusion  : 

i) C=A

ii) C>A

Conclusion: 

i) C<A

ii) C>A

2.Statement : P>Q=R<S

   Conclusion :

i)  P≤S

ii) P>S

Conclusion :

i) Q>S

ii) Q=S

3.Statement : M<N≥O≥P

Conclusion: 

i)  P<N

ii) P=N

Conclusion:     

i)  P>N

ii) P=N

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