Propositional Logic

Logic is a formal method of reasoning. Logic can be symbolically represented in many ways such as propositional logic, digital logic, Boolean algebra etc. One such way of doing so is propositional logic. The propositional logic represents logic through propositions and logical connectives. Proposition is an elementary atomic sentence that may either be true or false. Propositions are of two type’s simple propositions and compound propositions. Simple proposition does not contain any other proposition as a part. It uses lower case letters. Compound proposition is the one with two or more simple propositions as parts. It is a part of simple proposition.

Operator is used to join the simple proposition to make the compound proposition. Different symbols are used to designate the sentential connectives. The different types of connectives or operators are disjunctive, conjunctive, conditional, bi-conditional, negation. Disjunctive connective is also known as OR and is represented by disjunction symbol. Conjunctive is also known as AND. It is represented by the conjunction symbol. Conditional connective is also known as ‘If - then’ or implication. Implication means if one argument is true then the other argument is true. Bi-Conditional is also known as if and only if or equivalence. Equivalence means either both are true or both are false. Negation is also called as NOT or unary operator. It is an operator that affects a single statement only and does not join two or more statements. Proposition that is always true is known as tautology. Contrapositive is conditional statement whose antecedent is the negation of the original consequent and whose consequent is the negation of the original antecedent.

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  • Q1

    Name the types of connectives used in propositional logic.

    Marks:1
    Answer:

    The types of connectives used in propositional logic are:
    i) Disjunctive
    ii) Conjunctive
    iii) Conditional
    iv) Bi-conditional
    v) Negation

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  • Q2

    What are the truth values of simple and compound proposition?

    Marks:1
    Answer:

    The truth value of a statement is its truth or falsity. Every simple and compound proposition takes either true value or false value.

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  • Q3

    Name two types of propositions.

    Marks:1
    Answer:

    The two types of propositions are:
    i) simple proposition
    ii) compound proposition

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  • Q4

    Define proposition?

    Marks:1
    Answer:

    It is an elementary atomic sentence that may either be true or false (no other value).

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  • Q5

    What is the meaning of the term Logic?

    Marks:1
    Answer:

    Logic is defined as the study of the principles of correct reasoning.

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