Truth Tables — Tautology, contradiction
Mathematical Reasoning
7
JEE Qs
8%
Hard
50
min
Always follow a systematic, column-by-column approach when constructing truth tables to avoid errors, especially for complex logical statements.
🧮 Key Formulas
✅ Key Points for JEE
- 1Systematically construct truth tables for compound statements by first listing all possible truth value combinations for individual propositions, then evaluating sub-expressions step-by-step.
- 2A compound statement is a Tautology if the final column of its truth table contains only 'T' (True) values.
- 3A compound statement is a Contradiction if the final column of its truth table contains only 'F' (False) values.
- 4For 'n' simple statements, there will be 2^n rows in the truth table, ensuring all possible combinations of truth values are covered.
- 5Pay close attention to the truth values of 'Implication (P => Q)' which is false ONLY when P is true and Q is false, and 'Biconditional (P <=> Q)' which is true only when P and Q have the same truth value.
⚠️ Common Mistakes
- ✕Incorrectly evaluating the truth value for implication (P => Q), especially when P is false (it's always true in such cases).
- ✕Errors in systematic column-by-column evaluation when building complex truth tables, leading to incorrect final truth values.
- ✕Mistakes in determining the total number of rows (2^n) or properly listing all combinations of truth values for multiple propositions.
📝 Practice Questions
See allQ68. Choose the correct answer from the options given below : (1) (A)-(IV), (B)-(III), (C)-(II), (D)-(I) (2) (A)-(III), (B)-(IV), (C)-(II), (D)-(I) (3) (A)-(III), (B)-(IV), (C)-(I), (D)-(II) (4) (A)-(III), (B)-(I), (C)-(IV), (D)-(II)
Q64. Choose the correct answer from the options given below : (1) (A)-(III), (B)-(IV), (C)-(II), (D)-(I) (2) (A)-(I), (B)-(III), (C)-(II), (D)-(IV) (3) (A)-(III), (B)-(IV), (C)-(I), (D)-(II) (4) (A)-(IV), (B)-(III), (C)-(I), (D)-(II)
Q63. Given below are two statements : In the light of the above statements, choose the correct answer from the options given below : (1) Both Statement I and Statement II are true (2) Statement I is false but Statement II is true (3) Statement I is true but Statement II is false (4) Both Statement I and Statement II are false
Q73.Negation of (p →q) →(q →p) is (1) (p~) ∨p (2) q ∧(~p) (3) (~q) ∧p (4) p ∨(~q)
Q73.Among the statements (S1) : (p ⇒q) ∨((~p) ∧q) is a tautology (S2) : (q ⇒p) ⇒((~p) ∧q) is a contradiction (1) Neither (S1) and (S2) is True (2) Both (S1) and (S2) are True (3) Only (S2) is True (4) Only (S1) is True
Q72.Which of the following statements is a tautology? (1) p →(p ∧(p →q)) (2) (p ∧q) →(~(p) →q) (3) (p ∧(p →q)) →~q (4) p ∨(p ∧q)
NCERT Chapters
- Class 11 Maths Ch 14: Mathematical Reasoning