Understanding Conditional Statements in Logic and Mathematics | The Implication of p → q

if p → q is true and p is true, then q is true

In logic and mathematics, the statement “p → q” represents a conditional statement or an implication

In logic and mathematics, the statement “p → q” represents a conditional statement or an implication. This statement can be read as “if p, then q” or “p implies q.”

The definition of a conditional statement is that it is only false when the hypothesis (p) is true but the conclusion (q) is false; otherwise, it is considered to be true. Therefore, when “p → q” is true and we know that p is true as well, then it follows that q must also be true. This is known as the law of detachment or modus ponens.

To summarize:
– If “p → q” is true,
– And if p is also true,
– Then q must be true.

This is a fundamental principle in logic and is often used in various proofs and reasoning in mathematics.

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