In logical reasoning, syllogism is an important topic. A syllogism is an inference drawn in which one proposition (the conclusion) follows of necessity from premises.
There are three kinds of syllogism: categorical, hypothetical and disjunctive. In a categorical syllogism, the major premise will state something that will be taken as an absolute starting point and the minor premise will be examined against this absolute starting point in order to infer the conclusion. An alternative name for the if/ then syllogism is the hypothetical syllogism. The disjunctive syllogism represents choice based like ‘either - or’ statement.
Effective methods step by step to solve syllogism:
Underline the number of variables given in statements and draw a Venn diagram while also connecting them with each other the way it has been mentioned in the statement.
* Follow the sequence of the question while drawing Venn diagram.
* Analyse the conclusion from the Venn diagram and deduce the right conclusion.
Model Questions
Directions (Q.s 1 - 5 ): In each question below are given some statements followed by some conclusions. you have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows/ follow from the given statements.
Give answer as,
A) Only I follows B) Only II follows
C) Both I and II follows D) Either I or II follows
E) Neither I nor II follows
1. Statements: Each flower is door.
Few doors are trucks.
Conclusions:
I. All trucks being flower is a possibility.
II. Some doors are flowers.
Given that, 'all flowers are doors', so 'some doors are flowers' can be concluded. Since, there is no negative terms in the statement part, all trucks being flower is a possibility also true.
Hence both conclusions I and II follows. Ans: C
2. Statements: 72% violins are carpets.
Almost carpets are magnets.
Conclusions:
I. At least some magnets are violins.
II. No violin is magnet.
Here, '72% (some) violins are carpets' and 'almost (some) carpets are magnets'. From these two statements, we cannot conclude definitely that 'some magnets are violins' and 'no violin is magnet'. But here, both of them forms as a complementary pairs. Hence, either conclusion I or II follows. Ans: D
3. Statements: All bars are coconuts.
Not a single coconut is mushroom.
Conclusions:
I. No mushroom is bar.
II. Some bars being mushroom is a possibility.
Given, 'all bars are coconuts' and 'not a single (no) coconut is mushroom'. From these two, we can conclude that 'no mushroom is bar'. Whereas, 'some bars being mushroom' won't be a possibility. Hence, only conclusion I follows. Ans: A
4. Statements: Mostly pink are green.
100% green are violet.
Conclusions:
I. Every green being pink is a possibility.
II. Some violet are pink is a possibility.
'Mostly (some) pink are green' and '100% (all) green are violet'. From the given statements, 'every (all) green being pink is a possibility' follows but 'some violet are pink is a possibility' is failure here as some violet are pink is a definite conclusion from the statement it shouldn't be placed under possibility. So, only conclusion I follows. Ans: A
5. Statements: 0% utensils are machines.
At most machines are bamboos.
Conclusions:
I. Some utensils are definitely not bamboo.
II. Some bamboo are definitely not utensils.
Given that, '0% (no) utensils are machines' and 'almost (some) machines are bamboos'. According to given statements we can conclude 'some bamboos are definitely not utensils'. So, conclusion II follows. But the conclusion I 'some utensils are definitely not bamboo'may be true or may not be, we cannot say definitely. So, here only conclusion II follows. Ans: B
Directions (Qs. 6 - 10): Below are given few statements followed by few conclusions. pick up the right conclusion that follows.
6. Statements:
Only wallet is helmet.
A few wallets are pumpkins.
None of pumpkins are gloves.
Conclusions:
I. No glove is helmet.
II. All wallets being pumpkins is a possibility.
III. Some wallets are definitely not pumpkins.
A) Only I and II follows
B) Only I and III follows
C) Only III follows
D) Only II and III follows
E) None of the above
Given, 'only wallet is helmet' in the statement, mentions definitely that no other elements will be helmets. As per this, conclusion I follows. From, second and third statements we conclude, 'some wallets are definitely not pumpkins'. All wallets being pumpkins won't be a possibility as 'all wallets' include 'helmets' which shouldn't maintain relation with other
entities except wallets. So, only conclusion I and III follows. Ans: B
7. Statements:
Every cucumber is grapes.
Only a few grapes are papaya's.
No Papaya is pineapple.
Conclusions:
I. All papaya being grapes is a possibility.
II. All grapes being papaya is a possibility.
III. Some cucumber being pineapple is a possibility.
A) Only I and II follows
B) Only I follows
C) Only III and I follows
D) Only II follows
E) All follows
Given, 'only a few grapes are papayas' nothing but few grapes are papayas and few of them are not definitely. From, all the given three statements, only conclusion I and III follows.
Ans: C
8. Statements:
Many trousers are engines.
Only engines are containers.
Only a few laptops are trousers.
Conclusions:
I. some laptops are containers.
II. All engines being trousers is a possibility.
III. No laptop is container.
A) Only I and III follows
B) Either I or III follows
C) Only II follows
D) Only III follows
E) None follows
The second statement 'only engines are containers' mentions no other elements will be containers as definite. So conclusion III follows. Here, conclusion I and II does not follow from the given statements. Ans: D
9. Statements:
Only a few cupboards are vessels.
Only a few pillows are vessels.
Some drums are cupboards.
Conclusions:
I. Some drums are pillows.
II. Some pillows are not drums.
III. All pillows being cupboards is a possibility.
A) Only III follows
B) Either I or II and III follows
C) Only II follows
D) Both I and III follows
E) All follows
From given all the three statements, conclusion I and II does not follow as definite, but forms as complementary pair's. Conclusion III follows directly as a definite conclusion according to the given statements. Hence, either conclusion I or II and III follows. Ans: B
10. Statements:
Some pins are not hats.
All hats are muffets.
Some chains are hats.
Conclusions:
I. No chain is muffet is a possibility.
II. All pins being muffets is a possibility.
III. Some hats are pins.
A) Only III follows
B) Only II follows
C) Both I and II follows
D) Only I follows
E) All follows
Explanation:
According to the given statements 'all hats are muffets' and 'some chains are hats', the first conclusion 'no chain is muffet is a possibility' will be failure. From the statement 'some pins are not hats', we cannot conclude that some hats are pins (to say here it as definite conclusion, it should satisfy from both definite and possibility figures with respect to given statements). Hence, only conclusion II follows. Ans: B
