Syllogism Questions [Doubt Cleareance thread]

Google

Give Answers:

(a) if only conclusion I follows
(b) if only conclusion II follows
(c) if either I or II follows
(d) if neither I nor II
(e) if both follow

1)
Statements:
(A) All teenagers go to cinema
(B) Raveesh doesn't go to cinema

Conclusions:
I. Raveesh is not a teenager
II. Going to cinema is not essential to be a teenager.

2)
Statements:
(A) Some rods are sticks
(B) some scales are rods

Conclusions:
I. some sticks are rods
II. some scales are sticks


Please give answers with explanation.

text book answers: 1-a
2-d

I am getting: 1-c
2-a

vijay_45

For Q1. Text book answer is correct.

Since Raveesh does not go to cinema, he is definitely not a teenager.

But it is not said that only teenagers go to cinema. Hence going to cinema is not essential to be a teenager. May be some elder people are also going to cinema.

Hence, only 1 follows. Answer-'a'

For Q2.
conclusion 2 does not follow; as it is very much possible that none scales are rods.
Conclusion 1 is also not always correct. Since there are 2 possibilities. one- some sticks are Rods and two- all sticks are rods.

Hence answer will be 'd'

Neyawn

@Google, in syllogism when you asked to draw a conclusion, you must remember that the conclusion must be necessary and definite and not merely possible or probably. That is, there must be 100% certainty of that thing happening. Even if there is some case where the conclusion doesnt hold, then the conclusion will not be true.

Neyawn

Look at Questions 2
There can be two cases. (I solve questions by Venn diagrams, which is good enough for most questions)

(A) Some rods are sticks
(B) some scales are rods

Are these possible:-
Diagram 1



And Diagram 2



Now See the conclusion:-
Conclusions: [Updated]
I. some sticks are rods - Possible - Yes , But Necessary - No (D2) ; Hence not certain- Necessary - Yes, some sticks will be rods.
II. some scales are sticks - Possible - Yes (Diagram 1) Necessary - No

Hence (d) if neither I nor II
Updated answer:-
(a) if only conclusion I follows

vijay_45

Look at Questions 2
There can be two cases. (I solve questions by Venn diagrams, which is good enough for most questions)

(A) Some rods are sticks
(B) some scales are rods

Are these possible:-
Diagram 1



And Diagram 2



Now See the conclusion:-
Conclusions:
I. some sticks are rods - Possible - Yes , But Necessary - No (D2) ; Hence not certain-
II. some scales are sticks - Possible - Yes (Diagram 1) Necessary - No

Hence (d) if neither I nor II

How does diagram 2 show that some sticks are not rods??

My understanding is that one can draw the circle of sticks completely within the circle of rods. This will ensure that some rods are sticks, but not some sticks (rather all sticks) are rods?

Google

@newman, vijay

I couldn understand.

If some rods are sticks then obviously some sticks must be rods

vijay_45

@newman, vijay

I couldn understand.

If some rods are sticks then obviously some sticks must be rods

No, it is not true that some sticks must be rods.

When you say some rods are sticks, it means some rods are not sticks as well and also possible that all sticks are rods.

When it is said that some sticks are rods, it means some sticks will also be not rods; but this will not be possible when all sticks are rods.

You draw a circle, anything which falls within the perimeter is rod. for statement 1: Some rods are sticks; there can be 2 possibilities. You can draw another circle for sticks which intersects the circle representing rods. In this case, the statement 1 is justified and conclusion 1 is also correct.

But in situation 2, you can draw a circle (for sticks) which is completely within the perimeter of Rod-circle. Here statement 1 is correct; however conclusion 1 is not correct. Since all sticks are rods.

Google

@newman, vijay

Thx guys. Got it!

robinhood1947

@vijay_45

In the last para of what you have written, I was confused with the last statement. When All sticks are Rods then Some Sticks will also be Rods right???

I second your answer but I doubt it will solve every question of that type.

It will helpful for us if you can throw some more light on these type of exceptions.

vijay_45

@vijay_45

In the last para of what you have written, I was confused with the last statement. When All sticks are Rods then Some Sticks will also be Rods right???

I second your answer but I doubt it will solve every question of that type.

It will helpful for us if you can throw some more light on these type of exceptions.

There is a difference between the statements "Some are ..." and "All are ....".

In case of "All Sticks are Rods". - There will be no stick which is not rod.

In case of "Some sticks are Rods": - It means Some sticks are definitely not rods.

There is a method which is more systematic. It is well explained in TIMES material. I would try to share those pages in evening (after reaching home from office).

alphaqsecc

@vijay_45 : I was anticipating those scanned pages. It'd be great if you squeeze time for that. Thanks!