Statements — Simple and compound
Mathematical Reasoning
7
JEE Qs
8%
Hard
40
min
Focus on clearly identifying whether a sentence can be assigned a definite true or false value to classify it as a statement, and meticulously break down compound statements into their simplest components and logical connectives.
✅ Key Points for JEE
- 1A mathematical statement (or proposition) must be a declarative sentence that is either true or false, but not both. Ambiguous sentences, questions, commands, or exclamations are NOT statements.
- 2Simple statements are those which cannot be broken down further into two or more statements. They are the atomic units of logical reasoning.
- 3Compound statements are formed by combining two or more simple statements using logical connectives: 'and' (∧), 'or' (∨), 'not' (~), 'if...then' (→), and 'if and only if' (↔).
- 4Identifying the individual simple statements and the connective(s) used is crucial for analyzing the truth value of a compound statement.
- 5Context is important; ensure the sentence has a definite truth value within the given mathematical context to qualify as a statement.
⚠️ Common Mistakes
- ✕Confusing sentences that are questions, commands, or exclamations with mathematical statements, as these lack a definite truth value.
- ✕Misidentifying simple statements within a compound one, especially when natural language phrasing is complex or contains implicit connectives.
- ✕Failing to recognize that a statement must have a clear and unambiguous truth value (true or false) without needing further information or context to decide.
📝 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