Seating Arrangements; Syllogism; Statements and Conclusions; Statements and Assumptions

Seating Arrangements

8.1 Linear Arrangement

People sitting in a row (single or double row).

Key Points:

Left/Right based on person's perspective (not viewer's)
"To the immediate right of A" = next seat on A's right side
"Two places to the left of B" = second seat on B's left side

8.2 Circular Arrangement

People sitting around a round table.

Key Points:

No absolute direction in circular arrangement
Fix one person, arrange others relative to them
"To the immediate left" in circular = clockwise direction

Opposite person = 180° across the table

8.3 Step-by-Step Method

Step 1: Read all clues carefully Step 2: Pick the most specific clue (fixes exact position) Step 3: Use elimination to fill remaining positions Step 4: Verify with all remaining clues

8.4 Types of Seating Questions

Type	What to Find
Who is sitting next to X	Direct neighbor
Who is sitting opposite to X	Person across the table
Who is 3rd from X's left	Count 3 seats in left direction
How many between X and Y	Count seats between them
Which direction X faces	Based on arrangement type

8.5 Tips for Circular Seating

If "facing the center" → left is ANTICLOCKWISE, right is CLOCKWISE
If "facing outward" → left is CLOCKWISE, right is ANTICLOCKWISE
Total arrangements of n around a circle = (n-1)!

Syllogism

9.1 What is Syllogism?

Syllogism = Deductive reasoning using categorical statements. Given two (or more) premises, draw valid conclusions.

9.2 Types of Categorical Statements

Type	Statement	Symbol
Universal Affirmative	All A are B	A+
Universal Negative	No A is B	A-
Particular Affirmative	Some A are B	I+
Particular Negative	Some A are not B	I-

9.3 Venn Diagram Method

All A are B → A circle completely inside B circle

No A is B → A and B circles completely separate

Some A are B → A and B circles overlap partially

Some A are not B → Part of A is outside B

9.4 Rules for Syllogism

Premises	Conclusion
All A are B + All B are C	All A are C ✓
All A are B + No B is C	No A is C ✓
Some A are B + All B are C	Some A are C ✓
Some A are B + No B is C	Some A are not C ✓
Some A are B + Some B are C	No definite conclusion
No A is B + No B is C	No definite conclusion

9.5 Complementary Pairs

In exam questions with "Either conclusion I or II follows":

One must be true in all possible diagrams
If both invalid individually but together they cover all possibilities → complementary pair
Typically: "Some X are Y" and "No X are Y" are complementary

9.6 Possibility-based Conclusions

"It is possible that..." type:

A possibility conclusion is true if it does NOT violate any premise
"All A are B is a possibility" when some A are B and nothing says not all

Statements and Conclusions

10.1 Concept

Given a statement (fact), determine which of the given conclusions logically follows.

10.2 Rules

Conclusion must directly follow from the statement
Do NOT use outside knowledge — only what the statement says
Implicit vs Explicit: Both can be valid
Conclusion should be stronger or equal to the statement, not weaker

10.3 Key Patterns

Overgeneralization (usually wrong):

Statement: "Some students failed the exam."

Wrong conclusion: "All students are weak."

Logical deduction (correct):

Statement: "Regular exercise reduces health risks."

Correct conclusion: "Exercise is beneficial for health."

Statements and Assumptions

11.1 What is an Assumption?

An assumption is something that is taken for granted (implied but not stated).

11.2 Rules

The assumption must be necessary for the statement to make sense
It should NOT be too obvious (definitional truth) or too far-fetched
The assumption supports the statement's action or claim

11.3 Examples

Statement: "Buy 2, get 1 free — at SuperMart."

Assumption 1: Customers are attracted by discount offers ✓
Assumption 2: SuperMart sells quality products ✗ (not assumed)
Assumption 3: There are customers who shop at SuperMart ✓