# logical reasoning : Premises and conclusion

  Given below are two premises ( A and B). Four conclusions are drawn from
them. Select the code that states validly
drawn conslusion(s) ( taking the premises individually or jointly)

Premises:
(A) Most of the dancers are physically fit
(B) Most of the singers are dancers.

Conclusions:
(a) Most of the singers are physically fit
(b) Most of the dancers are singers.
(c) Most of the physically fit persons are dancers.
(d) Most of the physically fit persons are singers.

Code:

(1) d and a
(2) a and b
(3) b and c
(4) c and d
`

which one is the right answer any why?

## my workout:

i think none of the answers are correct because some or the singers are physically fit and only some of the dancers are singers

and only some of the physically fit persons are singers/dancers.

but not too sure.

• I don't know what they mean by taking the premises individually. If both premises are true, I think you are correct. – saulspatz Jul 9 '18 at 6:32

If premise:

50.1% of the dancers are physically fit and 50.1% of the singers are dancers.

Conclusions:

< 50% (a) Most of the singers are physically fit.

> 50% (b) Most of the dancers are singers.

> 50% (c) Most of the physically fit persons are dancers.

< 50% (d) Most of the physically fit persons are singers.

Code: (1) d and a (2) a and b (3) b and c (4) c and d

• How do you get "most of the dancers are singers?" Say there are 100 dancers and 10 singers; everyone is physically fit; all of the singers are dancers. Premises A) and B) are satisfied. It is not true that most of the dancers are singers. – saulspatz Jul 9 '18 at 6:30
• You didn't explain your reasoning, In fact, your answer is wrong. – Bram28 Jul 9 '18 at 14:26

i think none of the answers are correct because some or the singers are physically fit and only some of the dancers are singers and only some of the physically fit persons are singers/dancers.

You are correct that you cannot infer any of the 4 claims, but your reasoning is incorrect.

The easiest way to show that the claims cannot be inferred is by constructing a concrete counterexample. Consider the Venn diagram below:

The numbers indicate how many people there are for each type, e.g. there are 5 people who are physically fit but who are neither dancers nor singers; there is 1 person who is a singer and a dancer, but not physically fit, etc.

If this is the situation, you will find that both premises A and B are true, but all of the possible conclusions a,b,c, and d are false. So, none of the conclusions can be inferred.

• An explanation that your answer is wrong is offered on CBSE NET July 2018 Paper-1 Set-P Answers with Explanations on Examrace Channel Part-2. – Rob Jul 9 '18 at 15:13
• @Rob She's hard to understand, but right at the start of going over this problem I do believe that she says that none of the conclusions can be inferred, which is compatible with my answer (did you look at my answer? Do you see how it makes all premises true and all conclusions false?) I think she tries to explain why a and b are most likely to be true, but that all depends on whatever numbers you are dealing with. That is, I can easily change the numbers so that c and d are true, and a and b are false. So, I totally agree with the OP: this was a terrible question! – Bram28 Jul 9 '18 at 15:23