Syllogism:
The syllogism is an essential part of all the papers which contain aptitude questions. It is generally a part of the competitive exams in the reasoning ability section, it plays a vital role in examinations sharing 3 or 4 marks out of the total marks. There are many ways of reaching the final solution to questions of syllogisms. The most popular and easily used method of all is using a Venn diagram. Based on the statements given in the question, one should draw all the possible diagrams and one with minimum overlapping will be taken. Finally, options that satisfy all conditions according to the Venn diagram will be considered.
Important points to remember:
- Only A is B can be rewritten as “All B are A”
- Only a few A are B can be written as ” Some A are B ” as well as ” Some A are not B”. This means that some part of A is fixed in that it is related to B but the rest part of A has no relation to B.
Direction: In the following question, some conclusions are given and some statements are given you have to take the given conclusions to be true even if they seem to be at variance with commonly known facts and then decide from which of the statements given in options make the conclusion given the statement definitely true.
1- Conclusions:
- All tomatoes being Fungus is a possibility.
- All cabbage being Fungus is a possibility.
1. Statement-I: All cabbage are tomato. No tomato is fungus. All beans are fungus.
2. Statement-II: All cabbage are tomato. No tomato is Beans. All beans are fungus.
3. Statement-III: Some cabbage are tomato. No tomato is fungus. All beans are fungus.
4. Statement-IV: No cabbage are fungus. No tomato is beans. All beans are fungus.
5. Statement-V: Some cabbage are tomato. No tomato is beans. No cabbage is fungus.
Answer:
We need no direct relation between tomatoes and fungus according to the first conclusion. Same as from the second conclusion no direct relation between cabbage and fungus so we get a possibility relation.
Statement-I: All cabbage are tomato. No tomato is fungus. All beans are fungus. (Direct relation is present, we will not get possibility case from this statement)
Statement-II: All cabbage are tomato. No tomato is Beans. All beans are fungus.
From the above Venn diagram, we can clearly say that conclusions first and second follow this statement.
Statement-III: Some cabbage are tomato. No tomato is fungus. All beans are fungus. (Direct relation is present, we will not get possibility case from this statement)
Statement-IV: No cabbage are fungus. No tomato is beans. All beans are fungus. (Direct relation is present, we will not get possibility case from this statement)
Statement-V: Some cabbage are tomato. No tomato is beans. No cabbage is fungus. (Direct relation is present, we will not get possibility case from this statement)
2- Conclusions:
- All mobile being gramophone is a possibility.
- No mobile is red FM.
- Some automobiles are mobile is a possibility.
1. Statement-I: All mobile are conditioner. No conditioner are gramophone. Some Gramophones are automobiles.
2. Statement-II: No mobile is gramophone. No conditioner is red FM. Some gramophones are automobiles. Some red FM are automobiles.
3. Statement-III: All mobile are conditioner. All conditioner is red FM. Some red FM are gramophones. Some gramophones are automobiles. Some automobiles are transistors.
4. Statement-IV: All mobile are conditioner. No conditioner is red FM. All red FM are gramophones. Some gramophones. are automobiles. Some automobiles are not transistors.
5. Statement-V: Some mobile are not conditioner. All conditioners are red FM. Some red FM are not gramophones are automobiles. Some automobiles are transistors.
Answer:
We need indirect relation (possibility case) between mobile and gramophone & automobiles and mobile. And direct relation (no case) between Mobile and red FM.
Statement-I: All mobile are conditioner. No conditioner are gramophone. Some Gramophones are automobiles.
We will get direct relation between mobile and gramophone, so here possibility case is not present.
Statement-II: No mobile is gramophone. No conditioner is red FM. Some gramophones are automobiles. Some red FM are automobiles.
We will get direct relation between mobile and gramophone, so here possibility case is not present.
Statement-III: All mobile are conditioner. All conditioner is red FM. Some red FM are gramophones. Some gramophones are automobiles. Some automobiles are transistors.
We get all mobile is red FM. So conclusion second is not satisfying.
Statement-IV: All mobile are conditioner. No conditioner is red FM. All red FM are gramophones. Some gramophones. are automobiles. Some automobiles are not transistors.
All the conclusion is satisfied by this statement:
Statement-V: Some mobile are not conditioner. All conditioners are red FM. Some red FM are not gramophones. Some gramophones are automobiles. Some automobiles are transistors.
We are not getting the second conclusion correct according to the given statement that no mobile is red FM.
3- Conclusions:
- Some oranges are triangle is a possibility.
- Some center are figure
- Some center are oranges
- Some figure are fanta.
1. Statement-I: All triangle are fanta. No fanta are oranges. All oranges are figure. All figure are center.
2. Statement-II: No triangle are fanta. No fanta are oranges. All oranges are figure. All figure are center.
3. Statement-III: Some triangles are fanta. Some fanta are oranges. All oranges are figure. All figure are center.
4. Statement-IV: Some triangles are fanta. Some fanta are oranges. No oranges is figure. No figure is center.
5. Statement-V: Some triangle are fanta. Some fanta are oranges. Some oranges is figure. Some figure is center.
Answer:
Statement-I: All triangle are fanta. No fanta are oranges. All oranges are figure. All figure are center.
Conclusion first is not following with the given statement.
Statement-II: No triangle are fanta. No fanta are oranges. All oranges are figure. All figure are center.
Conclusion fourth is not following with the given statement.
Statement-III: Some triangle are fanta. Some fanta are oranges. All oranges are figure. All figure are center.
Conclusion first is not following with the given statement.
Statement-III: Some triangle are fanta. Some fanta are oranges. All oranges are figure. All figure are center.
All the conclusion follows with the given statement.
Statement-IV: Some triangle are fanta. Some fanta are oranges. No oranges is figure. No figure is center.
The conclusion second is not following with the given statement.
Statement-V: Some triangle are fanta. Some fanta are oranges. Some oranges is figure. Some figure is center.
Conclusion third is not following with the given statement.
4-Conclusions:
- Some eagle are being cattle is a possibility.
- Some toy are being eagle is a possibility.
1. Statement-I: All cattle are donkeys. Some eagle are donkeys. No toy is eagle.
2. Statement-II: All cattle are donkeys. No eagle is donkey. All toy are cattle.
3. Statement-III: Some cattle are donkeys. Some eagle is donkey. No toy is eagle.
4. Statement-IV: Some cattle are donkeys. Some eagle is donkey. Some toy is eagle.
5. Statement-V: Some cattle are donkeys. Some eagle is donkey. All toy is eagle.
Answer:
Statement-I: All cattle are donkeys. Some eagle are donkeys. No toy is eagle.
The conclusion second is not following with the given statement.
Statement-II: All cattle are donkeys. No eagle is donkey. All toy are cattle.
Conclusion first is not following with the given statement.
Statement-III: Some cattle are donkeys. Some eagle is donkey. No toy is eagle.
The conclusion second is not following with the given statement.
Statement-IV: Some cattle are donkeys. Some eagle is donkey. Some toy is eagle.
The conclusion second is not following with the given statement.
Statement-V: Some cattle are donkeys. Some eagle is donkey. All toy is cattle.
All conclusions follow the given statement.
Direction (5-10): In each of the following questions two or three statements are given and these are followed by two conclusions. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read the conclusion and then decide which of the given conclusion logically follows the statements.
Given Answer:
- Option A- If only (1) conclusion follows
- Option B- If only (2) conclusion follows
- Option C- If either (1) or (2) conclusion follows
- Option D- If neither (1) nor (2) conclusion follows
- Option E- If both (1) and (2) conclusion follows
5- Statement: Only a few children are fruit lovers. No fruit lover is fair. All fair are a dog lovers.
Conclusion:
- All fruit lover is children is a possibility.
- All Fair are dog lover is a possibility.
Answer: Option A
According to the statement, only a few children are fruit lovers so, all fruit lovers can be children but all children cant be fruit lovers.
6- Statement: Only pink are red. Some pink are violet. Some violet are not black.
Conclusion:
- All black being red is a possibility.
- Some black are pink is a possibility.
Answer: Option B
According to the statement, it is clear that red has relation only to pink.
7- Statement: All tree are branches. Some branches are root. Only a few root are steam.
Conclusion:
- All steam are not branches.
- Some root being tree is a possibility.
Answer: Option B
8- Statement: All house are great. Only a few men are female. No female is child
Conclusion:
- Only house is child
- Only men is female.
Answer: Option D
According to the statement, child doesn’t have only a relation with the house it can have a relation with other objects. The same condition applied to the conclusion second.
9- Statement: Only pen is ink. Some rifle is a pentagon. No pentagon is hexagon.
Conclusion:
- Some hexagon is not ink
- Some hexagon is not ink is a possibility.
- All hexagon is ink is a possibility.
Answer: Option A
According to the statement, the ink has only relation with the pen. Rest all objects cant have a relation with ink. So conclusion first is correct.
10- Statement: All Vegetables are green. All green are leaves. No leaves are flowers. Only a few flowers is bud.
Conclusion:
- All buds are Vegetables.
- Only a few Vegetables are flowers.
- Only green is bud.
Answer: Option D
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