Introduction to logical reasoning - Understanding conditiona...

Learning Outcomes

By completing this article, you will be able to identify, diagram, and manipulate conditional statements as they appear in LSAT logical reasoning questions. You will understand the difference between sufficient and necessary conditions, recognize formal logic structures, accurately form contrapositives, and apply these concepts to typical LSAT reasoning tasks. You will also be aware of common logical errors involving conditional reasoning.

LSAT Syllabus

For LSAT, you are required to understand conditional logic and how it applies to argument structure and question types. In your revision and practice, focus on:

• recognising and diagramming "if-then" statements (conditional logic)
• distinguishing between sufficient and necessary conditions and identifying their indicators
• forming contrapositives correctly
• applying conditional reasoning to LSAT questions, such as parallel reasoning, strengthen, weaken, and assumption problems
• avoiding common logical fallacies involving conditionals (e.g., confusion of necessary and sufficient)

Test Your Knowledge

Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision.

1. Which of the following are necessary condition indicators?
   1. only if
   2. unless
   3. must
   4. then
2. Which of the following statements are true?
   1. The contrapositive of "If A, then B" is "If not B, then not A".
   2. The inverse of a conditional statement always retains its logical validity.
   3. The sufficient condition guarantees the necessary condition.
   4. "Unless" introduces a sufficient condition in formal logic.

3. What logical flaw is present in concluding "If X, then Y. Y is true, so X must also be true"?

4. True or false? "If not A, then not B" is logically equivalent to "If B, then A".

Introduction

Conditional statements and formal logic are central to many LSAT logical reasoning questions. Conditional reasoning—using "if-then" statements—appears in argument structures, assumption problems, and questions requiring you to identify logical parallels or spot flaws. Understanding the proper structure and interpretation of conditional logic is essential for accurate analysis and avoiding common errors under exam pressure.

Conditional Statements: Form and Indicators

A conditional statement claims that if one condition (the sufficient condition) is met, then another condition (the necessary condition) must also be met. These statements are often phrased as "If A, then B".

Key Term: conditional statement
A logical claim stating that if a sufficient condition is true, then a necessary condition must also be true.

Sufficient and Necessary Conditions

It is essential to distinguish between sufficient and necessary conditions for LSAT reasoning. The sufficient condition is enough by itself to guarantee the necessary condition. The necessary condition is required for the sufficient condition to occur, but on its own does not guarantee the sufficient condition.

Key Term: sufficient condition
The "if" part of a conditional; a circumstance that guarantees the necessary condition follows.

Key Term: necessary condition
The "then" part of a conditional; a circumstance that must be present if the sufficient condition occurs.

Indicator Words

• Sufficient condition indicators: if, when, whenever, all, each, every, any, people who
• Necessary condition indicators: only if, must, unless, requires, depends on, always, needs, in order to

How to Diagram Conditional Statements

For efficiency in the LSAT, diagramming is recommended. For "If A, then B", use “A → B”. This shows that A is sufficient for B; B is necessary for A.

Contrapositive

Every conditional statement has a contrapositive with the same logical meaning. Form the contrapositive by negating and reversing both parts: "If A, then B" becomes "If not B, then not A" (¬B → ¬A).

Key Term: contrapositive
A restatement of a conditional, formed by reversing and negating both sides; logically equivalent to the original.

Worked Example 1.1

Statement: "If a student completes every assignment, they will earn an A."

What can you validly infer if Jamal earns less than an A?

Answer:
We can infer that Jamal did not complete every assignment. The contrapositive is: "If a student does not earn an A, then they did not complete every assignment."

The Inverse and Converse: Logical Mistakes

• Converse: "If B, then A" (not logically equivalent to "If A, then B")
• Inverse: "If not A, then not B" (not logically equivalent to "If A, then B")

The only guaranteed valid transformation is the contrapositive.

Exam Warning

Do not confuse a statement with its converse or inverse. The only transformation logically equivalent to a conditional is its contrapositive.

Common Conditional Triggers on the LSAT

Pay attention to phrases such as "only if", "unless", and "without". These require care in translation:

• "Only if" introduces a necessary condition: "You can enter only if you have a ticket" → "If you enter, you have a ticket" (Enter → Ticket).
• "Unless" can often be translated as "if not": "Unless A, B" becomes "If not A, then B".

Worked Example 1.2

Statement: "You will pass the exam only if you submit the application."

Which is the correct conditional diagram?

Answer:
If you pass the exam, then you have submitted the application. (Pass → Submit).

Compound Conditionals: "And" / "Or"

Logical connectors matter:

• "If X and Y, then Z" means both X and Y are needed for Z.
• "If W, then X or Y" means at least one of X or Y must occur for W to lead to the result.

Negating "and" and "or":

• The contrapositive of "If A and B, then C" is "If not C, then not A or not B".
• The contrapositive of "If A or B, then C" is "If not C, then not A and not B".

Worked Example 1.3

"If the car won't start or the lights are dim, then the battery is dead."

What is the contrapositive?

Answer:
If the battery is not dead, then the car starts and the lights are not dim.

Recognizing Conditional Flaws

A common LSAT flaw is confusing sufficient and necessary conditions—assuming the necessary condition guarantees the sufficient condition (affirming the consequent). For example:

"If a law is just, then it is fair. The law is fair. Therefore, it is just." This is invalid.

Key Term: affirming the consequent
Incorrectly concluding that the truth of the necessary condition guarantees the sufficient condition.

Worked Example 1.4

Argument: "If someone is a judge, then they are a lawyer. Rachel is a lawyer. Therefore, Rachel is a judge."

Identify the flaw.

Answer:
This argument affirms the consequent. While all judges are lawyers, not all lawyers are judges. Being a lawyer is necessary, but not sufficient, to be a judge.

Conditional Chains and Deductions

On advanced questions, you may need to link multiple conditionals.

• If A → B, and B → C, then A → C.
• The contrapositive of A → C is ¬C → ¬A.

Worked Example 1.5

Given: "If a contract is signed, then it is binding. If binding, then enforceable."

What can you infer if a contract is not enforceable?

Answer:
Contrapositives: Not enforceable → Not binding → Not signed. So, the contract was not signed.

Revision Tip

When you see multiple "if-then" rules, chain them for deductions and diagram contrapositives for greater flexibility.

Application to LSAT Question Types

Conditional logic is found in:

• Parallel reasoning: Finding arguments with the same structure.
• Flaw questions: Identifying conditional errors.
• Necessary/sufficient assumption: Understanding the gap between conditions.
• Grouping games: Following "if", "only if", and "unless" rules.

Summary

Key Point Checklist

This article has covered the following key knowledge points:

• Conditional statements are "if-then" claims with sufficient and necessary conditions.
• The contrapositive is the only logically equivalent transformation of a conditional.
• Indicator words ("if", "only if", "unless") must be interpreted accurately.
• Converse and inverse of a conditional are not logically equivalent.
• Common flaw: affirming the consequent—assuming the necessary condition guarantees the sufficient.
• Compound conditionals ("and", "or") affect how you form contrapositives.
• Multiple conditional rules can be chained for deductions.

Key Terms and Concepts

• conditional statement
• sufficient condition
• necessary condition
• contrapositive
• affirming the consequent