Conditional Statements

What is a conditional statement?

A statement that can be written in "If-Then" form.
Example: If it rains, then the ground is wet. (If p, then q)

What is the hypothesis in a conditional statement?

The part following "If."

What is the conclusion in a conditional statement?

The part following "Then."

What is the converse of a conditional statement?

The statement formed by switching the hypothesis and conclusion.
Example: If the ground is wet, then it rains. (If q, then p)

What is the inverse of a conditional statement?

The statement formed by negating both the hypothesis and conclusion.
Example: If it does not rain, then the ground is not wet. (If not p, then not q)

What is the contrapositive of a conditional statement?

The statement formed by switching and negating both the hypothesis and conclusion.
Example: If the ground is not wet, then it did not rain. (If not q, then not p)

What is a counterexample in a conditional statement?

• An example that disproves the conditional by showing the hypothesis is true and the conclusion is false.
  Example: If it rains but the ground is covered by a tarp, the ground is not wet. (p is true, but q is false)

What is a biconditional statement?

• A statement that is true when both the conditional and its converse are true; written as "if and only if."
  Example: The ground is wet if and only if it rains. (p if and only if q)

• What does the symbol "→" represent in logic?