# Worked Examples: Type III

In each of the questions below are given three statements followed by four conclusions A, B, C and D. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follow from the given statements disregarding commonly known facts.â€‹

St. Iâ€”All teachers are doctors.

St. IIâ€”All doctors are engineers.

St. IIIâ€”All engineers are students.

Con Aâ€”Some students are teachers.

Con Bâ€”All doctors are students.

Con Câ€”Some engineers are teachers.

Con Dâ€”All doctors are teachers.

- Only A and B follow
- Only A and C follow
- Either A or B and C follows
- Either B or D follows
- Only A, B and C follow

Conclusion A is a mediate inference of statements I and III. These two statements do not have a middle term.

So, it is not possible to draw conclusion directly. We should first draw a conclusion from statement I and II and then relate this conclusion to statement III to draw the final conclusion. From statements I and II, we can draw the conclusion â€˜All teachers are engineersâ€™. On relating this conclusion with statement III, we notice that â€˜Some students are teachersâ€™ is true. So, conclusion A follows.

Conclusion B is a mediate inference of statements II and III. This conclusion complies with all the requirement. Hence, it follows.

Conclusion C is a mediate inference of statements I and II. As this conclusion also complies with all the requirement, it follows.

Conclusion D is an immediate inference of statement I. The term doctors is distributed in the conclusion, but the said term is undistributed in statement I. Hence, it does not follow.

Thus, conclusions A, B and C follow.

Answer: (5)

Analysis with Venn diagram.

S has some area in common with T. So, A follows.

Since D lies entirely within S, B follows.

Since E has some area in common with T, C also follows.

Since D does not lie entirely within T, D does not follow.

Answer: (5)

St Iâ€”Some grains are pulses.

St IIâ€”All vegetables are fruits.

St IIIâ€”All pulses are vegetables.

Con Aâ€”Some grains are vegetables.

Con Bâ€”All vegetables are pulses.

Con Câ€”All fruits are grains.

Con Dâ€”All vegetables are grains.

- Only A and B follow
- Only B follows
- Only A and D follow
- Only D follows
- Only A follows

Conclusion A is a mediate inference of statements I and III. Pulses is the middle term in these two statements and this term is distributed in statement III. One of the statements is particular. The conclusion is also particular. Both the statements are affirmative. The conclusion is also affirmative. Thus, the conclusion complies with all the requirements. Hence, it follows.

Conclusion B is an immediate inference of statement III. The term â€˜vegetablesâ€™ is distributed in the conclusion, but it is undistributed in statement III. Hence, this conclusion does not follow.

Conclusion C is a mediate inference of statements I and II. Since one of the statements is particular, the conclusion should be particular. As this conclusion is universal, it does not follow.

Conclusion D is a mediate inference of statements I and III. Since one of the statements is particular, the conclusion should be particular. As this conclusion is universal, it does not follow.

Thus, only conclusion A follows.

Answer: (5)

Analysis with Venn diagram.

The statements are represented in Venn diagram. As seen from the diagram, only conclusion A follows.

Answer: (5)

St Iâ€”Some ships are boats.

St IIâ€”All boats are submarines.

St IIIâ€”Some submarines are yatches.

Con Aâ€”Some yatches are boats.

Con Bâ€”Some submarines are boats.

Con Câ€”Some submarines are ships.

Con Dâ€”Some yatches are ships.

- All follow
- Only B and C follow
- Only C follows
- Only either C or D follows
- None of these

Conclusion A is a mediate inference of statements II and III. The middle term â€˜submarinesâ€™ is not distributed. Hence, this conclusion does not follow.

Conclusion B is an immediate inference of statements II. It complies with all the requirements. Hence, it follows.

Conclusion C is a mediate inference of statements I and II. As it complies with all the requirements, it follows.

Conclusion D is a mediate inference of statements I and III. Since both these statements are particular, no conclusion follows. Hence, conclusion D does not follow.

Thus, only conclusions B and C follow.

Answer: (2)

Analysis with Venn diagram.

The statements I, II and III are represented in the form of Venn diagram.

As seen in the diagram, both the conclusions B and C follow. Conclusion A and D do not follow.

Answer: (2)