Section 2.2 Analyze Conditional Statements

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Section 2.2Analyze Conditional Statements
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What is an if-then statement?

• If-then statements can be used to clarify
  statements that may seem confusing.
• These statements are logic statements.
• Logic statements are important in many different
  types of professions.

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Examples

1. If the sun shines, then the grass will grow.
2. If I live in NJ, then I live on the east coast.
3. If the month is January, then next month is
   February.

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• These if-then statements are called conditional
  statements or conditionals.
• Conditional Statement A logical statement that
  has two parts.
• In general, these conditionals are written
• If p, then q or p q.
• Where p is the hypothesis and
• q is the conclusion.

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Lets take a look back at our examples

1. If the sun shines, then the grass will grow.
2. If I live in NJ, then I live on the east coast.
3. If the month is January, then next month is
   February.

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• Converse Exchange the hypothesis and conclusion
  of the conditional.
• The converse of p q is q p.
• Conditional If I live in NJ, then I live on the
  east coast.
• Converse If I live on the east coast, then I
  live in NJ.

True!
False!
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• Write the converse of the following statement and
  decide if it is true or false
• Conditional If two angles are adjacent, then
  they have a common side.
• Converse If two angles have a common side, then
  they are adjacent.

FALSE!!
? CAD and ? BAD share a common side, but they are
not adjacent angles.
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• The denial of a statement is called a negation.
• p represents not p

3.) This is geometry. This is not geometry. 4.)
Today is not Thursday. Today is Thursday.
1.) An angle is obtuse. An angle is not
obtuse. 2.) A puppy is a dog. A puppy is not a
dog.
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• The inverse of a conditional can be formed by
  negating both the hypothesis and conclusion.
• p q

If-then Statement If two angles are vertical,
then they are congruent. Inverse If two angles
are not vertical, then they are not congruent.
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• Contrapositive can be formed by negating the
  hypothesis and conclusion of the converse of the
  given conditional.
• Whoa! What does that mean????!!!
• q p

If-then statement If two angles are vertical,
then they are congruent. Contrapositive If two
angles are not congruent, then they are not
vertical. Is the contrapositive of this statement
true or false???
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Quick Review

• If-then statement If p, then q.
• Converse If q, then p.
• Inverse If p, then q.
• Contrapositive If q, then p.

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Lets put it all together!

• If-then statement If you live in Red Bank, then
  you live in New Jersey.
• Converse If you live in New Jersey, then you
  live in Red Bank.
• Inverse If you do not live in Red Bank, then you
  do not live in New Jersey.
• Contrapositive If you do not live in New Jersey,
  then you do not live in Red Bank.

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Equivalent Statements

• A conditional statement and its contrapositive
  are either both true or false.
• The converse and inverse are either both true or
  both false.
• When two statements are both true or both false,
  they are called equivalent statements.

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Biconditional Statements

• When a conditional statement and its converse are
  both true, you can write them as a biconditional
  statement.
• Biconditional Statement A statement that
  contains the phrase if and only if.

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Rewrite as Biconditional Statements

• 1.) Rewrite the definition of right angle as a
  biconditional statement.
• An angle is a right angle if and only if the
  measure of the angle is 90 degrees.