Mathematical and Logical Reasoning

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A mathematically acceptable statement is a sentence that is either true or false but not both. It has a definite truth value. Example: 'The capital of India is New Delhi' is a statement (true) 'An ap

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If p is a statement, then the negation of p is denoted by ~p and read as 'not p'. Truth Table for Negation: Statement p | Negation ~p True | False False | True Example: If p: 'Fire is hot

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A compound statement with 'and' is made up of two or more component statements connected by 'and'. Truth conditions: • TRUE only when ALL component statements are true • FALSE if ANY component statem

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Inclusive OR: True when at least one component is true (allows both to be true) Exclusive OR: True when exactly one component is true (not both) Inclusive OR example: 'Students who have Biology OR Ch

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Quantifiers are phrases like 'there exists' and 'for all' used in mathematical statements. 'There exists' (∃): Means at least one such object exists Example: 'There exists a rectangle whose all sides

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'If p then q' is an implication denoted as p ⇒ q (p implies q) Key points: • If p is true, then q must be true • If p is false, we cannot conclude anything about q • p is called the hypothesis/antece

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The contrapositive of 'if p then q' is 'if ~q then ~p' Original: If a number is divisible by 9, then it is divisible by 3 Contrapositive: If a number is not divisible by 3, then it is not divisible b

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The converse of 'if p then q' is 'if q then p' Original: If a number is divisible by 10, then it is divisible by 5 Converse: If a number is divisible by 5, then it is divisible by 10 Important: The