7.1 CONDITIONAL AND BICONDITIONAL

STATEMENTSBY: JAY BASILGO

MARC OVILLEDANNAH PAQUIBOT

CONDITIONAL STATEMENTSEXAMPLE: “If two distinct lines intersect, then they intersect at exactly one point.”

CONDITIONAL STATEMENTS

• If – then statements•Consists of two parts: - if , hypothesis - then, conclusion

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.

MORE EXAMPLES

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

MORE EXAMPLES

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

THE CONVERSE, INVERSE, AND CONTRAPOSITIVE OF A CONDITIONAL

STATEMENTIt 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 qi. Converse: If q, then p.

ii. Inverse: If not p, then not q.iii. Contrapositive: If not q, then p.

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.

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

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.

INVERSE

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

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.

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

EXAMPLEa. 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.

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.

EXAMPLEa.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