# Worked Examples: Type II (More Than Two Conclusions are Given)

St. Iâ€”All cats are dogs.

St. IIâ€”No dog is black.

Con Aâ€”No black thing is cat.

Con Bâ€”No cat is black.

Con Câ€”Some black things are cats.

Con Dâ€”All dogs are cats.

- None follows
- Only D follows
- Only A follows
- Only A and B follow
- None of these

Since statement II is negative, the conclusion should also be negative (rule 7). Hence, conclusions C and D do not follow. Now in conclusion A, both the terms â€˜blackâ€™ and â€˜catsâ€™ are distributed. These terms are also distributed in the statements. So conclusion A follows. Similarly, conclusion B also follows.

Hence, we can conclude that only conclusions A and B follow.

Answer: (4)

Analysis with Venn diagram.

From the above diagram, we observe that no black thing is cat and no cat is black. Hence, only conclusions A and B follow.

St. Iâ€”Some parrots are mangoes.

St. IIâ€”All mangoes are apples.

Con Aâ€”All apples are mangoes.

Con Bâ€”All parrots are apples.

Con Câ€”Some parrots are apples.

Con Dâ€”Some mangoes are parrots.

- Only A and B follow
- All follow
- Only C and D follow
- Only B and C follow
- None follows

Since one of the premises is particular, the conclusion should be particular. Therefore, conclusions A and B do not follow. Conclusion C is particular and it is a mediate inference. Conclusion D is an immediate inference drawn from statement I. Both conclusions C and D follow.

Answer: (3)

Analysis with Venn diagram.

From the diagram, we notice that some parrots are apples and some mangoes are parrots. Hence, both the conclusions C and D follow.

St. Iâ€”All stars are planets.

St. IIâ€”All planets are clocks.

Con Aâ€”All planets are stars.

Con Bâ€”All stars are clocks.

Con Câ€”All clocks are planets.

Con Dâ€”Some clocks are stars.

- Only C, B and D follow
- Only A and B follow
- None follows
- All follow
- Only B and D follow

Since both the premises are affirmative, the conclusion should be affirmative (rule 8).

Conclusion A is an immediate inference drawn from premise I. The term â€˜planetsâ€™ is distributed in conclusion A without being distributed in premise I. So, conclusion A does not follow.

In conclusion B, the term â€˜starsâ€™ is distributed and this term is distributed in premise I also. So, conclusion B follows.

In conclusion C, the term â€˜clocksâ€™ is distributed without being distributed in any of the premises. So, conclusion C does not follow.

Conclusion D can be derived from conclusion B. So, conclusion D also follows.

Answer: (5)

Analysis with Venn diagram.

From the diagram, we observe that only conclusions B and D follow.

St. Iâ€”All typists are stenographers.

St. IIâ€”Some stenographers are girls.

Con Aâ€”All girls are stenographers.

Con Bâ€”All girls are typists.

Con Câ€”Some typists are girls.

Con Dâ€”No typist is a girl.

- Only A follows
- Only B and C follow
- Only either B or C follows
- Only either C or D follows
- None follows

Since the middle term is not distributed even once in the premises, no conclusion follows (rule 2). Conclusions C and D contradict each other. Both of them cannot be false simultaneously. When conclusion C is true, conclusion D is definitely false. When conclusion D is true, conclusion C is definitely false. Hence, either conclusion C or conclusion D follows.

Answer: (4)

Analysis with Venn diagram.

From the diagram, we notice that either conclusion C or conclusion D follows.