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DISCRETE MATHEMATICS module 1 (manoj)

truth tables

Gottipalli
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DISCRETE MATHEMATICS module 1 (manoj)

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  1. DISCRETE MATHEMATICSMODULE-1 GottipalliManoj(220101120226) Guided by:- Dr.Santosh Kumar Bhal

  2. Contents:- • The truth values of the propositions p and q • Negation. • Conjunction. • Disjunction. • Implication. • Inverse. • Converse. • Contrapositive.

  3. What is propositions ? • A proposition is a collection of declarative statements that has either a truth value "true” or a truth value "false". A propositional consists of propositional variables and connectives. • “A statement is not a proposition if we cannot decide whether it is true or false.

  4. Negation:- • In discrete mathematics, negation can be described as a process of determining the opposite of a given mathematical statement. For example: Suppose the given statement is “Saidoes not like choclates". Then, the negation of this statement will be the statement “Sailikes choclates".

  5. Conjunction. • A conjunction is a statement formed by adding two statements with the connector AND. The symbol for conjunction is '∧' which can be read as 'and'. When two statements p and q are joined in a statement, the conjunction will be expressed symbolically as p ∧ q. • Conclusion:- If both the statements are true then p ∧ q is true

  6. Disjunction:- • A disjunction is a compound statement formed by joining two statements with the connector OR. The disjunction "p or q" is symbolized by p ∨ q. • CONCLUSION:- A disjunction is false if and only if both statements are false; otherwise it is true

  7. Implication:- • Conditional statements are also called implications. An implication is the compound statement of the form “if p, then q.” It is denoted p⇒q, which is read as “p implies q.” • CONCLUSION:- It is false only when p is true and q is false, and is true in all other situations

  8. IF P→Q IS THE IMPLICATION, CONVERSE:-The converse statement is notated as q→p(if q, then p). The original statements switch positions in the original “if-then” statement. INVERSE:-The inverse statement assumes the opposite of each of the original statements and is notated ∼p→∼q (if not p, then not q). CONTRAPOSITIVE:-:-The contrapositivestatement assumes the opposite of each of the converse statements and is notated ∼q→∼p (if not p, then not q).

  9. Thank you………..

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