Validity

• How valid and invalid arguments differ from true/false statements.
• To test validity using truth tables, Venn diagrams, and counterexamples.
• To apply rules of inference: modus ponens, modus tollens, hypothetical syllogism.
• To analyse short arguments in Class 11 reasoning and CLAT-style logical deduction.

Level 1 — Foundations

Verbal: An argument = premises + conclusion. Valid = if premises were all true, conclusion must be true. Validity does not guarantee true premises.

Sound argument: Valid + all premises actually true.

Rules of inference:

Invalid patterns (memorise):

• Affirming consequent: P→Q, Q ⊢ P ✗
• Denying antecedent: P→Q, ¬P ⊢ ¬Q ✗

Counterexample: One scenario where premises true and conclusion false disproves validity.

Level 2 — Exam depth

Categorical syllogisms: All A are B; All B are C ⇒ All A are C (valid). "Some A are B; All B are C ⇒ Some A are C" — valid with careful reading.

Venn validity check: Shade regions inconsistent with conclusion; if diagram allows violation, invalid.

Strong vs weak (inductive): Reasoning notes focus on deductive validity — certainty, not probability.

Hidden premise: "Ravi failed; he did not study" assumes failure→lack of study — often invalid without that premise stated.

Exam strategy: Formalise in symbols first; then apply MT/MP; faster than verbal debate.

Test argument validity

Premises: (1) If it snows, schools close. (2) Schools did not close.
Conclusion: It did not snow.
Form: S→C, ¬C ⊢ ¬S — **Modus tollens — valid.**

Find counterexample to invalid form

Affirming consequent: If you are a doctor, you studied science. Maya studied science. Therefore Maya is a doctor.
Counter: Maya studied science in BA — premise "studied science" true, conclusion false. **Invalid.**

• Distinguish valid vs sound in one sentence each.
• Formalise: "Either tea or coffee; not tea; so coffee."
• Why is denying the antecedent invalid? Give counterexample.
• Stretch: Two premises, both true, conclusion false — can argument be valid?

Revision tip: Revisit adjacent topics in Logical Deduction before mixed practice on Validity.

Open the Practice tab for graded questions on Validity.

Learn the four core valid forms (MP, MT, HS, DS) by name and pattern — many exams recycle them with new vocabulary. For invalid arguments, one counterexample row is sufficient proof. Distinguish truth of conclusion from validity in every review session; exam distractors exploit this confusion. When premises are in English, symbolise first, argue second.

Validity training strengthens verbal argument sections — modus tollens appears in weaken-by-counterexample items. Truth tables provide mechanical backup when intuition falters on two-premise arguments. Legal-style inference questions ("must be true") share validity's no-counterexample standard. Debate judges penalise affirming the consequent — recognising the pattern in your own rebuttals prevents self-defeat.