Syllogisms

1. 1

   Statements:
   (1) Some leaves are kites.
   (2) Some leaves are flowers.

   Conclusions:
   (I) Some flowers are not kites.
   (II) All leaves are kites.

   Take the statements to be true, however odd they sound. Which conclusion follows?

   Question 1

   AOnly conclusion I follows BOnly conclusion II follows CBoth conclusions follow DNeither conclusion follows

   Answer and working

   Answer DD

   Conclusion I need not hold: every one of the flowers may be kites. Conclusion II need not hold: some leaves may lie outside kites. So: Neither conclusion follows.

2. 2

   Statements:
   (1) All stones are papers.
   (2) Some papers are not planes.

   Conclusions:
   (I) Some stones are not planes.
   (II) Some planes are papers.

   Take the statements to be true, however odd they sound. Which conclusion follows?

   Question 2

   AOnly conclusion I follows BOnly conclusion II follows CBoth conclusions follow DNeither conclusion follows

   Answer and working

   Answer DD

   Conclusion I need not hold: every one of the stones may be planes. Conclusion II need not hold: planes and papers need not overlap at all. So: Neither conclusion follows.

3. 3

   Statements:
   (1) Some doors are flowers.
   (2) Some doors are fans.

   Conclusions:
   (I) Some flowers are not fans.
   (II) Some fans are not doors.

   Take the statements to be true, however odd they sound. Which conclusion follows?

   Question 3

   AOnly conclusion I follows BOnly conclusion II follows CBoth conclusions follow DNeither conclusion follows

   Answer and working

   Answer DD

   Conclusion I need not hold: every one of the flowers may be fans. Conclusion II need not hold: every one of the fans may be doors. So: Neither conclusion follows.

4. 4

   Statements:
   (1) Some trees are doors.
   (2) No flowers are doors.

   Conclusions:
   (I) Some doors are not flowers.
   (II) Some trees are flowers.

   Take the statements to be true, however odd they sound. Which conclusion follows?

   Question 4

   AOnly conclusion I follows BOnly conclusion II follows CBoth conclusions follow DNeither conclusion follows

   Answer and working

   Answer AA

   Conclusion I holds in every diagram the statements allow. Conclusion II need not hold: trees and flowers need not overlap at all. So: Only conclusion I follows.

5. 5

   Statements:
   (1) All tables are rings.
   (2) No birds are rings.

   Conclusions:
   (I) Some tables are rings.
   (II) Some birds are not tables.

   Take the statements to be true, however odd they sound. Which conclusion follows?

   Question 5

   AOnly conclusion I follows BOnly conclusion II follows CBoth conclusions follow DNeither conclusion follows

   Answer and working

   Answer CC

   Conclusion I holds in every diagram the statements allow. Conclusion II holds in every diagram the statements allow. So: Both conclusions follow.

6. 6

   Statements:
   (1) Some fans are not lamps.
   (2) No lamps are cups.

   Conclusions:
   (I) Some lamps are not cups.
   (II) No cups are fans.

   Take the statements to be true, however odd they sound. Which conclusion follows?

   Question 6

   AOnly conclusion I follows BOnly conclusion II follows CBoth conclusions follow DNeither conclusion follows

   Answer and working

   Answer AA

   Conclusion I holds in every diagram the statements allow. Conclusion II need not hold: cups and fans may overlap. So: Only conclusion I follows.

7. 7

   Statements:
   (1) No bottles are roads.
   (2) No trees are roads.

   Conclusions:
   (I) Some trees are not roads.
   (II) Some roads are not trees.

   Take the statements to be true, however odd they sound. Which conclusion follows?

   Question 7

   AOnly conclusion I follows BOnly conclusion II follows CBoth conclusions follow DNeither conclusion follows

   Answer and working

   Answer CC

   Conclusion I holds in every diagram the statements allow. Conclusion II holds in every diagram the statements allow. So: Both conclusions follow.

8. 8

   Statements:
   (1) Some doors are not tables.
   (2) All doors are rivers.

   Conclusions:
   (I) No rivers are doors.
   (II) Some rivers are not tables.

   Take the statements to be true, however odd they sound. Which conclusion follows?

   Question 8

   AOnly conclusion I follows BOnly conclusion II follows CBoth conclusions follow DNeither conclusion follows

   Answer and working

   Answer BB

   Conclusion I need not hold: rivers and doors may overlap. Conclusion II holds in every diagram the statements allow. So: Only conclusion II follows.

9. 9

   Statements:
   (1) No flowers are watches.
   (2) All planes are flowers.

   Conclusions:
   (I) Some watches are not planes.
   (II) Some watches are not flowers.

   Take the statements to be true, however odd they sound. Which conclusion follows?

   Question 9

   AOnly conclusion I follows BOnly conclusion II follows CBoth conclusions follow DNeither conclusion follows

   Answer and working

   Answer CC

   Conclusion I holds in every diagram the statements allow. Conclusion II holds in every diagram the statements allow. So: Both conclusions follow.

10. 10

    Statements:
    (1) Some fans are trees.
    (2) Some fans are buses.

    Conclusions:
    (I) Some fans are not trees.
    (II) Some buses are not fans.

    Take the statements to be true, however odd they sound. Which conclusion follows?

    Question 10

    AOnly conclusion I follows BOnly conclusion II follows CBoth conclusions follow DNeither conclusion follows

    Answer and working

    Answer DD

    Conclusion I need not hold: every one of the fans may be trees. Conclusion II need not hold: every one of the buses may be fans. So: Neither conclusion follows.

More reasoning: Number and letter series, Coding and decoding, Analogies, Odd one out, Blood relations, Direction sense.