what is a biconditional students will be able to: 1.rewrite compound sentences in conditional form...
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What is a Biconditional
Students will be able to:1. Rewrite compound sentences in conditional form
2. Find the biconditional of a conditional3. Tell when/why a biconditional is true
Why is the following statement called a hidden conditional?
“My parents get mad when I don’t do my homework”The hypothesis and a conclusion are hidden.
“If I don’t do my homework, then my parents get mad
If a polygon has four sides, then the shape is a quadrilateral
p: A polygon has four sides q: The shape is a quadrilateral
If a polygon has four sides then the shape is a quadrilateral and if the shape is a
quadrilateral then the polygon has four sides
A polygon has four sides if and only if the shape is a
quadrilateral
1) Write p q in words
2) Write q p in wordsIf the shape is a quadrilateral, then the polygon has four sides( ) ( )p q q p Write in words3
)
What is a biconditional?
A polygon has four sides if and only if the shape is a
quadrilateral.
This type of statement is called a biconditional.
A biconditional is formed by combining two simple
statements using the words “if and only if”.
Symbol: p q
Definition:
p: School is not in session q: It is the weekend.
Write the biconditional statement in words.
School is not in session if and only if it is the weekend.
p q
p q p q q p
T
T
T
T
T
T
T
T
T
T T
T
F
F F
F F
F
F
F
A biconditional is true when p and qhave the same truth values
p q
General Truth Table for a BICONDITIONAL
(p q) (q p )
T T= T
F F= T
p: The car stops q: There is a red light
Write the biconditional statement in words.
The car stops if and only if there is a red light
p q
This biconditional statement is FALSE because “If the car stops then there is a red light,” is not always true.
p: A polygon has four right angles
q: A polygon is a square
3. Create a biconditional statement
A polygon has four right angles if and only if it is a square
1. Translate pq in wordsIf a polygon has four right angles then it is a square
2. Translate qp in words
If a polygon is a square then it has four right angles
Note: ( ) ( )p q q p p q
Regents Prep Logic Website
www.regentsprep.org/Regents/math/tables/PracAnd.htm
1) What is the symbol for a biconditional?
2) When is a biconditional true?