Inferences: Logical Reasoning Notes for AILET

Logical Reasoning – Inferences

AILET – Logical Reasoning Section (Topic: Inferences)

1. Simple Explanation

Inference is the logical step that connects given facts (premises) to a new statement (conclusion).

Deductive inference: If the premises are true, the conclusion must be true.
Inductive inference: The conclusion is likely, but not guaranteed.
Abductive inference: The most plausible explanation given limited data.

In the AILET context, you’ll often be asked to:

Question Type	What You Must Do
Conclusion	Identify the statement that necessarily follows from the premises.
Assumption	Spot the unstated premise that must hold for a conclusion to be valid.
Inference	Find the logical bridge that links premises to a new fact or implication.

2. Key Points to Remember

Category	Essentials	Tips
Logical Structure	Premise → Inference → Conclusion	Visualise as a chain: Premises → Inference → Conclusion
Types of Inferences	1. Deductive 2. Inductive 3. Abductive	Deductive → “must be true”; Inductive → “likely”; Abductive → “most plausible”.
Common Question Formats	• “Which of the following is a valid inference?” • “What is the assumption?” • “Which statement follows from the given premises?”	Read each option carefully; eliminate clearly false ones early.
Checking Validity	1. Assume all premises are true. 2. Does the conclusion logically follow?	Use truth tables or simple reasoning checks.
Avoiding Common Mistakes	• Assuming the conclusion is stated verbatim. • Choosing an inference that only could be true, not necessarily true. • Ignoring that some inferences might be overly strong (not supported by all premises).	Always ask: “Is this conclusion forced by every premise?”
Time‑Saving Tricks	• Look for “only if” / “if and only if” phrases: they often hint at deduction. • “All” / “No” statements → universal or universal negative premises → strong deductions. • “Some” → weaker, possible inductive inference.	Highlight keywords: all, no, only, must, cannot, somewhere.

3. Worked Example

Question

Given Premises

All students who study hard get good grades.

Sarah is a student who studies hard.

Which of the following is a valid inference?
A. Sarah will be happy.
B. Sarah is a good student.
C. Sarah gets good grades.
D. Sarah will study hard next year.
E. Sarah’s friends study hard.

Step‑by‑Step Solution

Step	Action	Reasoning
1	Identify premises	Premise 1 is a universal conditional: “If studies hard → good grades.” Premise 2 states the antecedent for Sarah.
2	Apply Modus Ponens	Premises 1 & 2 together give: “Sarah gets good grades.”
3	Match with options	Option C (“Sarah gets good grades”) is exactly the conclusion.
4	Check other options	A, B, D, E do not logically follow from the premises.
5	Answer	C

Explanation of Valid Inference

Modus Ponens: If P → Q and P is true, then Q must be true.
Here, P = “Sarah studies hard”, Q = “Sarah gets good grades”.

4. Quick Revision Summary

Item	What to Recall
Definition	Logical bridge from premises to a new statement.
Main Types	Deductive (must be true), Inductive (likely), Abductive (most plausible).
Common Formats	Conclusion, Assumption, Inference questions.
Key Verbs	Must, could, may, cannot, only if, if and only if.
Logical Rules	Modus Ponens, Modus Tollens, Disjunctive Syllogism, Hypothetical Syllogism.
Tips	• Highlight keywords. • Assume premises true. • Test if conclusion is forced by all premises. • Eliminate obviously false options first.

Remember: In inferences you’re looking for the logical link. If the link can be made only by using all given premises, it’s a valid inference. If it can be made by some but not all, it’s either an assumption or inductive inference—usually not the answer in AILET (unless the question explicitly asks for it).

Final Thought

Practice by converting each premise into a formal conditional statement, then apply the classic inference rules. The more you practice, the quicker you’ll spot the “must‑be” conclusion in any logical reasoning passage. Happy studying!