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The logical connective "IF-THEN" is also known as:a.Conjunctionb.Disjunctionc.Negationd.Implication

Question

The logical connective "IF-THEN" is also known as:

a. Conjunction
b. Disjunction
c. Negation
d. Implication

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Solution

The logical connective "IF-THEN" represents a conditional statement that connects two propositions in a way that expresses a dependency between them.

  1. Understanding Logical Connectives: Logical connectives are used in propositional logic to form compound statements from simpler ones. The main types include conjunction (AND), disjunction (OR), negation (NOT), and implication (IF-THEN).

  2. Definition of Implication: The "IF-THEN" statement is specifically known as an implication. In logical terms, if we denote two propositions as P P and Q Q , the statement "IF P P THEN Q Q " is represented as P    Q P \implies Q . This means that if P P is true, then Q Q must also be true.

  3. Examining the Options:

    • a. Conjunction: Represents the logical AND, which is true only if both propositions are true.
    • b. Disjunction: Represents the logical OR, which is true if at least one of the propositions is true.
    • c. Negation: Represents the logical NOT, which negates the truth value of a proposition.
    • d. Implication: Represents the logical IF-THEN, which is true unless a true proposition leads to a false one.
  4. Conclusion: By analyzing the definitions, it is clear that the "IF-THEN" logical connective is best represented by "Implication."

Final Answer

The logical connective "IF-THEN" is also known as d. Implication.

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