09.	+Conditional,+Converse,+Inverse+and+Contrapositive+Statements

**Conditional, Converse, Inverse and Contrapositive Statements**

Conditional- A conditional statement is usually expressed in "if, then" form and has two parts to it, the hypothesis and the conclusion. For example: If a animal is a dog(hypothesis), then it has four legs (conclusion). Conditional statements can be true or false, but in this case the conditional is true.

Converse- The converse is the conditional backward, the the conclusion first and then the hypothesis. If an animal has four legs (conclusion), then it is a dog (hypothesis). Like the conditional the converse, inverse, and the contrapositive can be true or false. The converse is false in this case because many other animals have four legs.

Inverse- The Inverse is the conditional statement negated. If an animal is not a dog, then it does not have four legs. This statement is false also because animals besides dogs have four legs.

Contrapositive- The contrapositive is the converse statement negated. If an animal does not have four legs, then it is not a dog. This statement is true.

Truth Values- When determining the truth value of a statement, the truth values of the conditional and he contrapositive are always the same while the converse and the conditional always have the same truth value.

Problems- a. Write the converse, inverse, and contrapositive. Tell whether the statements are true or false:

1. If two two lines are parallel, then they never intersect.

2. If two angles are complementary, then the sum of their measure is 90 degrees.

3. If a number is divisible by 4, then it is divisible by 2.  Solutions: a) 1. Converse- If two lines never intersect, then they are parallel. False, the lines could be skew lines, lines which never intersect Inverse- If two lines are not parallel, then they intersect. False, the lines could be skew lines, lines which never intersect. Contrapositive- If two lines intersect, then they are not parallel. True

2. Converse- If the sum of two angles measures 90 degrees, then the angles are complementary. True Inverse- If two angles are not complementary, then their sum does not measure 90 degrees. True Contrapositive- If the sum of two angles is not 90 degrees, then the angles are not complementary. True

3. Converse- If a number is divisible by 2, then it is divisible by 4. False, a number like 6 is divisible by two, but not divisible by 4. Inverse- If a number is not divisible by 4, then it is not divisible by 2. False, 10 is not divisible by 4, but is divisible by 2. Contrapositive- If a number is not divisible by two, then it is not divisible by 4. True

http://hotmath.com/hotmath_help/topics/converse-inverse-contrapositive.html http://www.jimloy.com/logic/converse.htm