Logical Reasoning - Cheat Sheet
Your last-minute revision companion for mastering logical reasoning concepts essential for CSE exams
Basic Logical Reasoning Concepts
Important facts
- Arguments consist of premises + conclusion
- Valid arguments have true conclusions if premises are true
- Premises must logically support the conclusion
- Assumptions are unstated but necessary premises
Key definitions
Logic
Example
Determining if 'All dogs bark, Spot is a dog, therefore Spot barks' is valid
Study of correct vs incorrect reasoning
Argument
Example
Scientists are brilliant; Jet is a scientist; Therefore, Jet is brilliant
Sequence of statements where one is supported by others (Premises + Conclusion)
Premise
Example
All cats are mammals (supporting the conclusion about Felix)
Statement that provides reason for accepting the conclusion
Conclusion
Example
Therefore, Jet is brilliant (drawn from the premises about scientists)
Statement that is established by the premises
Assumption
Example
Hidden premise that connects stated premises to conclusion
Unstated premise in the argument
Diagrams to know
- Venn diagrams for categorical statements
- Flowcharts for conditional reasoning
- Linear diagrams for ordering problems
Types of Reasoning
Important facts
- Deductive: If premises true, conclusion must be true
- Deductive: Uses 'valid' or 'invalid' terminology
- Inductive: Conclusion is probably supported by premises
- Inductive: Uses terms like 'probably', 'likely', 'possibly'
- Inductive arguments can become stronger/weaker with additional premises
Key definitions
Deductive Reasoning
Example
All zombies crave flesh; Anne is zombie; Therefore Anne craves flesh
Starts with general statement to reach specific conclusion (top-down approach)
Inductive Reasoning
Example
Most shelter dogs are happy; Max is shelter dog; Therefore Max is probably happy
Starts from specific observations to broad generalizations (bottom-up approach)
Diagrams to know
- Top-down flow for deductive reasoning
- Bottom-up flow for inductive reasoning
Syllogisms
Formulas
If A is B, and B is C, then A is C
Meaning
A=major term, B=middle term, C=minor term
Watch out
Middle term must appear in both premises but NOT in conclusion
When to use
When connecting two categorical statements
Important facts
- Major term: appears in premise and is predicate of conclusion
- Minor term: appears in premise and is subject of conclusion
- Middle term: appears in both premises, NOT in conclusion
- Disjunctive options must be mutually exclusive
- Conditional syllogisms follow if-then logic patterns
Key definitions
Categorical Syllogism
Example
All dogs bark; Sparky is dog; Therefore Sparky barks
Argument with two premises connecting major and minor terms through middle term
Disjunctive Syllogism
Example
Donut is glazed or filled; Not filled; Therefore glazed
Either/or argument where one option is eliminated
Conditional Syllogism
Example
If rain, then wet; It's raining; Therefore wet
If-then argument with conditional premises
Diagrams to know
- Syllogism structure diagrams
- Venn diagrams for categorical syllogisms
Reactions or equations
If A then B; A is true; Therefore B is true
Note
Valid form of conditional reasoning
Conditions
Modus Ponens - affirming the antecedent
If A then B; B is false; Therefore A is false
Note
Valid form of conditional reasoning
Conditions
Modus Tollens - denying the consequent
Venn Diagrams
Important facts
- 'All A are B' - circle A completely inside circle B
- 'Some A are B' - circles A and B overlap partially
- 'No A are B' - circles A and B are completely separate
- Can combine multiple statements in single diagram
- Use overlapping regions to find valid inferences
Key definitions
Universal Statement (All)
Example
All Filipinos are Asians - Filipino circle inside Asian circle
Complete inclusion - entire first set inside second set
Particular Statement (Some)
Example
Some women are doctors - overlapping circles
Partial inclusion - sets overlap but neither completely contains the other
Negative Statement (No)
Example
No fish are mammals - separate circles
Complete exclusion - sets do not overlap at all
Diagrams to know
- All statements - nested circles
- Some statements - overlapping circles
- No statements - separate circles
- Combined statement diagrams
Ordering and Sequencing
Important facts
- Draw linear diagrams for ordering problems
- Start with most definitive relationships first
- Use symbols like > < to show relationships
- Check consistency of all given relationships
- Identify who is first, last, middle positions
Key definitions
Linear Ordering
Example
A is taller than B, B taller than C, arrange by height
Arranging items in single line based on given relationships
Relative Position
Example
Juan is between Maria and Pedro in line
Position of item compared to others using comparative relationships
Diagrams to know
- Linear arrangement diagrams
- Relationship mapping charts
Problem-Solving Strategies
Important facts
- Working backwards: reverse all operations
- Organized lists help with multiple conditions
- Diagrams clarify complex spatial/temporal relationships
- Always verify solution against all given conditions
- Choose strategy based on problem type
Key definitions
Working Backwards
Example
Virgilio has P3232 left after series of transactions, find initial amount
Start from final result and reverse operations to find initial value
Organized List
Example
List all two-digit numbers with digit sum 15, eliminate by other conditions
Systematic enumeration and elimination of possibilities
Diagram Method
Example
Draw distance-time diagram for meeting problems
Visual representation to map relationships and solve complex problems
Diagrams to know
- Backwards flow charts
- Elimination tables
- Distance-time diagrams
Must remember
- Deductive reasoning: general to specific, must be valid if premises true
- Inductive reasoning: specific to general, conclusions are probable
- Syllogism structure: major term (predicate), minor term (subject), middle term (connector)
- Venn diagrams: All = nested circles, Some = overlapping, No = separate
- Working backwards: reverse all operations from final result
- Conditional syllogisms: If A then B; affirm antecedent or deny consequent
- Middle term appears in both premises but NOT in conclusion
- Arguments = premises + conclusion; check if conclusion logically follows
- Linear ordering: draw diagrams, start with most definitive relationships
- Always verify solutions against ALL given conditions
Last minute tips
- For syllogisms, identify the three terms first: major, minor, middle
- In Venn diagrams, 'All A are B' means circle A goes INSIDE circle B
- For ordering problems, draw a line and place items step by step
- Watch for key words: 'all' vs 'some' vs 'no' change diagram structure completely
- In conditional statements, you can only conclude if antecedent is affirmed or consequent is denied
Comparison tables
Deductive vs Inductive Reasoning
| Aspect | Deductive | Inductive |
|---|---|---|
| Direction | General to specific | Specific to general |
| Approach | Top-down | Bottom-up |
| Certainty | Certain if premises true | Probable conclusion |
| Terminology | Valid/Invalid | Probably/Likely/Possibly |
| Strength | Fixed validity | Can strengthen/weaken |
Types of Syllogisms
| Type | Structure | Example |
|---|---|---|
| Categorical | A is B, B is C, so A is C | All dogs bark; Spot is dog; So Spot barks |
| Disjunctive | A is B or C, A is not C, so A is B | Donut glazed or filled; Not filled; So glazed |
| Conditional | If A then B, A true, so B true | If rain then wet; Raining; So wet |
Diagrams
Logical Reasoning Concept Map
Overview of all logical reasoning concepts and their relationships
Argument Analysis Process
Step-by-step process for analyzing logical arguments
Venn Diagram Construction Guide
Process for constructing and using Venn diagrams in logical reasoning