How to pass DMGT JNTU R23 in easyway | prepositional logic | Truth Tables | DMGT MathematicalLogic |

Discrete mathematics, often perceived as challenging, becomes manageable by analyzing the syllabus and focusing on key topics. Truth tables form a foundational concept essential for exams; understanding their values is crucial. Sets and relations are straightforward when mastered with equivalent relations, recurrent relations, matrices including inverse ones—these can secure significant marks in assessments. Mathematical induction combined with algorithms and recursion forms another critical unit to perfect for scoring well within limited exam durations.

The unit on logic and proofs introduces seven key topics: propositional logic, equivalence, predicates with quantifiers (including nested ones), rules of inference, proof methods, and strategies. A foundational concept is the 'propositional statement,' defined as a declarative sentence that can be either true or false. Examples include "Delhi is the capital of India" (true) versus "Delhi is the capital of America" (false). Non-declarative sentences like questions or commands do not qualify as propositional statements.

Compound propositions are formed by connecting two or more statements using logical connectives. Examples include negation, disjunction, conditional, biconditional, tautology, and contradiction. For instance: "Today is Sunday" and "Today it is raining" can be combined into a compound proposition through these connectives to analyze their truth values under different conditions.

Negation is the logical opposite of a given proposition. If 'p' represents a statement, its negation, denoted as "not p," expresses the contrary meaning. For example, if "Today is Monday" is true, then its negated form would be "Today is not Monday." This concept helps to construct and analyze statements by considering their opposites.

Conjunction is a logical operation represented by 'and,' combining two propositions, p and q. The conjunction of p and q is true only when both are true; otherwise, it results in false. For example, if "p" represents "Today is Sunday," and "q" means "It is raining," the statement 'p AND q' holds true only if both conditions occur simultaneously. Disjunction operates with an 'or' logic between propositions p or q. It yields a result of true when at least one proposition (either p or q) holds as true but becomes false solely when both are false.

A conditional statement, denoted as 'p implies q,' is read as "if p then q." In this structure, 'p' represents the hypothesis and 'q' signifies the conclusion. The truth value of a conditional depends on its components: it is false only when the hypothesis (p) is true but the conclusion (q) is false; in all other cases, it remains true. This logical construct forms a foundation for understanding implications within reasoning.

A biconditional statement represents a double implication, meaning both directions of the relationship between two propositions must hold true. It is expressed as "p if and only if q," signifying that p implies q and q implies p simultaneously. In its truth table, the result is true only when both statements share identical truth values—either both are true or false; otherwise, it results in false. This logical construct ensures equivalence between conditions by requiring mutual agreement for validity.