Syllogisms! 2

Logic Level 1

Given below are three statements followed by three conclusions. Take the three statements to be true even if they vary from commonly known facts. Read the statements and decide which conclusions follow logically from the statements.

Statements:
1. All actors are musicians.
2. No musician is a singer.
3. Some singers are dancers.

Conclusions:
1. Some actors are singers.
2. Some dancers are actors.
3. No actor is a singer.

Answer Choices:
a) Only conclusion 1 follows.
b) Only conclusion 2 follows.
c) Only conclusion 3 follows.
d) At least 2 of the conclusions follows.

a) b) c) d)

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3 solutions

Pranshu Gaba
Jul 5, 2016

It is a good idea to use draw Venn diagram in such problems. The following is a Venn diagram illustrating the above statements.

From the Venn diagram, we can see that

  1. No actor is a singer, since they have no area in common. Hence, Conclusion 1 is false.
  2. No dancer is an actor, since they have no area in common. Hence, Conclusion 2 is also false.
  3. No actor is a singer. Hence, Conclusion 3 is true.

The statements do imply that singers does not intersect musicians, but there is no statement that implies that dancers does no intersect with musicians and actors. The problem with conclusion 2 is that it is still a possibility buy does not follow directly from just the given statements.

Kunal Kantaria - 4 years ago

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That's right, from the given information, we can only conclude conclusion 1 to be true with certainty. The given information is not sufficient whether statement 2 is true or not.

Pranshu Gaba - 4 years ago

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I agree with Kunal. If we construct a Venn diagram like above in a problem solution, some people might be mistaken and consider it to be what follows logically from the info in the question.

Raivat Shah - 2 years, 8 months ago

right, conclusion 2 could be correct as well

Ben Ji - 1 year, 1 month ago

Was contemplating getting a Brilliant subscription but this one has not been fixed at least in the 10 months it was flagged as wrong...

Kobus Engelbrecht - 3 months, 4 weeks ago

conclusion 3 is used for distraction

Akhash Raja Raam
Jun 28, 2016

The only statement which can be said with certainty is conclusion 3! If all actors are musicians, it means that only some (not all) musicians are actors. If no musician is a singer, then no actor is a singer too. If some singers are dancers then some actors or musicians who are not singers could be dancers too. In all the three conclusions, the third one is the one we can say is true with more certainty than the earlier two conclusions. So the correct choice is C!

Can you explain why?

Calvin Lin Staff - 4 years, 11 months ago

The venn diagram is incorrect, as dancers' group may intersect with the actors' and/or musicians', but it also may not. The position of the dancers' group is an incognito and hence, cannot be drawn with just one combination of venn diagrams. To have a correct drawing, one must draw three combinations of venn diagrams: 1. One with dancers' diagram intercepting musicians and not actors, and the rest equal to the one drawn above 2. One with the dancers' diagram intercepting musicians and actors, and the rest equal to the one drawn above 3. The third is exactly like the one drawn above by Pranshu Gaba. The statements that are correct are the ones that satisfy the conditions for ALL the THREE different combinations of Venn diagrams. The only statement (conclusions) that satisfies the conditions of all the three combinations is conclusion 3.

Bobba Bobba - 6 months ago

Did it in the edit! Was a little busy that i forgot to elaborate the answer on this question earlier. Thanks for the reminder!

Akhash Raja Raam - 4 years, 11 months ago

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