Logic Statements

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What is a conditional statement?

Back

A conditional statement is a logical statement that has two parts: a hypothesis (if part) and a conclusion (then part). It is often written in the form 'If P, then Q'.

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What is the contrapositive of a conditional statement?

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The contrapositive of a conditional statement 'If P, then Q' is 'If not Q, then not P'. It is logically equivalent to the original statement.

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What is the inverse of a conditional statement?

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The inverse of a conditional statement 'If P, then Q' is 'If not P, then not Q'. It is not logically equivalent to the original statement.

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What is the law of syllogism?

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The law of syllogism states that if 'If P, then Q' and 'If Q, then R' are both true, then 'If P, then R' is also true.

Front

What does the symbol '∧' represent in logic?

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The symbol '∧' represents a conjunction, which means 'and'. It is used to combine two statements that are both true.

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What is a conjunction in logic?

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A conjunction is a compound statement formed by combining two statements with the word 'and'. It is true only if both statements are true.

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What is a disjunction in logic?

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A disjunction is a compound statement formed by combining two statements with the word 'or'. It is true if at least one of the statements is true.

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What is a biconditional statement?

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A biconditional statement is a logical statement that combines two conditional statements, written as 'P if and only if Q'. It is true when both statements are either true or false.

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What is the difference between a tautology and a contradiction?

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A tautology is a statement that is always true regardless of the truth values of its components, while a contradiction is a statement that is always false.

Front

What is the truth table for a conjunction?

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The truth table for a conjunction (P ∧ Q) shows that it is true only when both P and Q are true.