Syllogism / Statements & Conclusions
Syllogism is a logical reasoning topic of the ADRE Grade IV paper in which two or more statements are given and the candidate has to decide which of the given conclusions follows from them. The statements are treated as true even if they seem unusual in real life, and the conclusions are tested only by logic. The topic needs no calculation and no general knowledge; it only needs correct reasoning with the help of simple set diagrams. Once the rules are understood, syllogism becomes one of the easiest and most scoring topics.
Meaning and Form
A syllogism consists of two parts: statements and conclusions. Statements are the given facts, and conclusions are the statements that may or may not follow. The four standard statement types are "All A are B", "Some A are B", "No A is B" and "Some A are not B". The task is to check whether each conclusion is definitely true on the basis of the given statements. A conclusion that is possible but not certain does not follow.
Basic Rules
- "All A are B" also means "Some B are A".
- "Some A are B" also means "Some B are A".
- "No A is B" also means "No B is A".
- "Some A are not B" does not convert.
- Two particular statements give no definite conclusion.
- Two negative statements give no definite conclusion.
The Venn Diagram Method
The safest way to solve a syllogism is to draw circles for the classes. For "All A are B", draw the circle of A inside the circle of B. For "No A is B", draw the two circles separately without any overlap. For "Some A are B", draw the circles overlapping so that some part is common. Then look at each conclusion and check whether it is true in every possible arrangement of the circles. If it is true in all arrangements, the conclusion follows; if it fails in even one arrangement, it does not follow.
Worked Example
Suppose the statements are "All pens are books" and "All books are bags". Then the circle of pens lies inside books, and books lie inside bags, so the conclusion "All pens are bags" definitely follows. But if the statements are "Some pens are books" and "Some books are bags", the pen and bag circles need not touch at all, so the conclusion "Some pens are bags" does not follow. This shows why every possible arrangement must be considered.
How This Topic Appears in the Examination
Syllogism usually appears as two to four objective questions of one mark each, often in a set of two statements followed by two or three conclusions. The candidate has to mark which conclusions follow. The questions are quick once the circle method is used. Because the same statements are used for several conclusions, drawing the diagram once saves time and prevents confusion.
Memory Tips
Always draw circles instead of trying to reason in words. Remember the two easy conversions: "All A are B" gives "Some B are A", and "Some A are B" gives "Some B are A". Treat a conclusion as following only when it is true in every possible diagram. For "possibility" questions, check whether the conclusion can be made true without contradicting the statements.
Common Mistakes to Avoid
- Using real-world knowledge instead of the given statements.
- Accepting a conclusion that is only possible, not certain.
- Forgetting to convert "All A are B" into "Some B are A".
- Drawing only one arrangement and not testing all cases.
- Trying to solve without a diagram and losing track.
How to Prepare This Topic
- Learn the four statement types and their conversions.
- Practise drawing Venn diagrams for every question.
- Solve possibility questions separately.
- Check each conclusion against every possible diagram.
- Practise daily until the rules become automatic.
More Solved Examples
Take the statements "All roses are flowers" and "Some flowers fade quickly". The rose circle lies inside the flower circle, and the fading part overlaps the flower circle. The conclusion "Some roses fade quickly" does not follow, because the overlapping part need not touch the rose circle. But the conclusion "Some flowers are roses" does follow, because every rose is a flower. In another example, from "No cat is a dog" and "All dogs are animals", the conclusion "Some animals are not cats" follows, because the dogs, which are animals, are definitely not cats. This shows how every conclusion must be tested against the diagram.
Advanced Tips for the Exam
Draw the diagram in more than one way when a conclusion is doubtful, and if the conclusion fails in any drawing, reject it. Remember the two useful conversions: "All A are B" gives "Some B are A", and "Some A are B" gives "Some B are A". For possibility conclusions, do not look for certainty; instead check whether the conclusion can be made true without contradicting the statements. Use short names for the classes to save time. Attempt the easy definite conclusions first and leave the possibility ones for the end.
Quick Revision Checklist
- Four statement types: All, Some, No and Some-not.
- Conversions of the All and Some statements.
- Two particular statements give no conclusion.
- Two negative statements give no conclusion.
- A conclusion follows only if it is true in every diagram.
- Possibility questions allow more than one arrangement.
Frequently Asked Questions
What is syllogism?
Syllogism is a reasoning topic in which statements are given and you must decide which conclusions definitely follow from them, treating the statements as true.
Should I use real-world knowledge in syllogism?
No. You must treat every statement as true and test the conclusions by logic alone, even if the statement seems unusual in real life.
What is the easiest method to solve syllogism?
The Venn diagram method. Draw circles for the classes and check whether the conclusion is true in every possible arrangement.
When does a conclusion definitely follow?
A conclusion follows only when it is true in every possible arrangement of the diagram. If it fails in even one arrangement, it does not follow.
What does "All A are B" imply?
It means every A is a B, and it also allows the valid conversion "Some B are A". It does not mean that all B are A.