Conditional and biconditional statements

Conditional and biconditional statements for grade 8

1. 7.1 Conditional and biconditional statements BY: Jay basilgo Marc oville Dannah paquibot

2. CONditional statements EXAMPLE: “If two distinct lines intersect, then they intersect at exactly one point.”

3. Conditional statements If – then statements Consists of two parts: - if , hypothesis - then, conclusion

4. More examples If two points lie in a plane, then the line containing them lies in the plane. Hypothesis: Two points lie in a plane. Conclusion: The line containing them lies in the plane.

5. More examples If 2(x+5) = 12, then X = 1. Hypothesis: Conclusion:

6. More examples A quadrilateral is a polygon . A prime number has 1 and itself as factors. A square is a rectangle.

7. The converse, inverse, and contrapositive of a conditional statement It is said that if a statement is true, its contrapositive is also true. Moreover, if the converse is true, its inverse is also true. Consider the statement: if p, then q Converse: If q , then p. Inverse: If not p , then not q . Contrapositive: If not q , then p.

8. converse To write the converse of a conditional statement, simply interchange the hypothesis and the conclusion. That is, the then part becomes the if part. Note that converse of a conditional statement is not always a true statement.

9. Example a. If m<A= 9, then m<A is a Rigth angle. Converse: If m<A is a right angle, then m<A = 90

10. Example B. The intersection of two distinct planes is a line. If-then: If two distinct planes intersect, then their intersection is a line. Converse: If the intersection of two figures is a line, then the figure are two distinct planes.

11. INverse To write the inverse of a conditional statement, simply negate both the hypothesis and conclusion.

12. EXAMPLE If m<A<90, then <A is an acute angle. INVERSE: If m<A is not 90, then <A is not an acute angle. If two distinct lines intersect, then they intersect at one point. INVERSE: if two distinct lines do not intersect, then they do not intersect at a point.

13. contrapositive To form the contrapositive of a conditional statement, first, get its inverse. Then, interchange its hypothesis and conclusion.

14. Example If m<A +m<B= 90, then <A and <B are complementary. Inverse: if m<A + m<B is not equal to 90, then <A and <B are complementary. Contrapositive: If <A and <B are not complementary, then m<A + B is not equal to 90.

15. Biconditional statement If a conditional statement and its converse are both true. Then they can be joined together into a single statement called biconditional statement. Then this is done by using the words if and only if.

16. EXAMPLE If a+7= 12, then a = 5. Conditional statement: if a+7 = 12, then a = 5 Converse statement : If a = 5, then a + 7 = 12 *Both the conditional statement and its converse are true statements. Hence, the biconditional statement is a+7 = 12 iff a =5