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## Section 2-1

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**Section 2-1**Conditional Statements**Conditional statements**• Have two parts: • Hypothesis (p) • Conclusion (q)**"If p, then q:” p q**When written in If-Then form… • The “If” part ALWAYS contains the hypothesis • The “Then” part ALWAYS contains the conclusion**Example #1**• If it is a Friday, then you will not have homework. it is a Friday Hypothesis (p): Conclusion (q): you will not have homework**Do not include the words “If” and “then” when naming**the hypothesis and conclusion!**Sometimes a conditional statement is written without using**"if" and "then".**Example #2**• Perpendicular lines intersect at right angles. Can rewrite: If two lines are perpendicular, then the lines intersect at right angles.**If two lines are perpendicular, then the lines intersect at**right angles. Hypothesis (p): two lines are perpendicular Conclusion (q): the lines intersect at right angles**counterexample**• an example that disproves a statement • Only need one counterexample to disprove a statement**Example #3**• If a number is odd, then it is divisible by 3. False Counterexample: 5 is odd and is not divisible by 3!**Conditional : p q**Converse : q p converse • formed by interchanging the hypothesis and conclusion of the conditional.**Example #4**• If two lines are perpendicular, then the lines intersect at right angles. Write the converse. If two lines intersect at right angles, then the lines are perpendicular.**inverse**• the negation of both the hypothesis and the conclusion of the conditional. • The denial of a statement is called a negation.**Conditional:p q**~ p ~ q Inverse: Read as not p then not q**Example #5**• If two lines are perpendicular, then the lines intersect at right angles. If two lines are not perpendicular, then the lines do not intersect at right angles. Inverse:**Converse: q p**~q ~p contrapositive • negation of both the hypothesis and conclusion of the converse Contrapositive: Read as not q then not p**Example #6**• If two lines are perpendicular, then the lines intersect at right angles. Write the converse. If two lines intersect at right angles, then the lines are perpendicular.**Then write the contrapositive.**If two lines do not intersect at right angles, then the lines are not perpendicular.**Equivalent statements**• Statements that are both true or both false**A conditional statement is equivalent to its contrapositive**Conditional = Contrapositive • The converse and inverse of any conditional statement are equivalent. Converse = Inverse