2-2+Biconditional+Statements

2-2 Biconditional Statements

http://www.mathgoodies.com/lessons/vol9/biconditional.html http://regentsprep.org/regents/math/geometry/GP1/bicon.htm

Biconditional Statements are statements written with the phrase "if and only if" (iff). Writing a biconditional statement is the same as writing a conditional statement and its converse together. If both the converse and conditional statement are true you can write a biconditional statement. You then need to combine the converse and the original statement to form a true biconditional statement. This section will teach you how to take a conditional statement and its converse and make it into a biconditional statement. (textbook pages 79-86)

Vocabulary:
 * perpendicular lines:** intersect at a right angle
 * A line perpendicular to a plane:** a line that intersects a plane in a point and is perpendicular to every line in the plane that intersects it.


 * biconditional statement:** a statement that contains the phrase "if and only if." (a conditional statement and the converse)

1) conditional: If the angles are supplementary, then the measures of the angles add up to 180 degrees converse: If the measures of the angles add up to 180 degrees, then the angles are supplementary biconditional: The angles are supplementary iff the measures of the angles add up to 180 degrees

2) conditional: If the animal is black, then it is a bird converse: If the animal is a bird, then it is black You can't write a biconditional statement because the converse and conditional are both not true counterexample: a blue bird is not black it is blue

3) conditional statement: If the team won, then they got a trophy converse: If the team got a trophy, then they won biconditional statement: The team won iff they got a trophy

Practice Problems: Write the converse of the statement and if it is true write a biconditional statement. If it is false write a counterexample. (Answers are at the bottom of the page).

1) CONDITIONAL: If i did my homework, then i get my allowance

2) CONDITIONAL: If x is prime, then x is odd

3) CONDITIONAL: If you shut off the water, then the water will stop coming out

4) If I'm chewing gum, then my mouth tastes like mint

Answers: 1) Converse: If i get my allowance, then i did my homework Biconditional: I did my homework iff i get my allowance

2) Converse: If x is odd, then x is prime Counterexample: 9 is odd and is not prime

3) converse: If the water stops coming out, then you shut off the water Biconditional: You shut off the water iff the the water stops coming out

4) Converse: If my mouth tastes like mint, then I'm chewing gum Counterexample: My mouth can taste like mint after i brush my teeth