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2.2 Notes
Name __________________
A ____________________ ____________________ is a logical statement that has two parts, a
______________________ and a ____________________.
Conditional statements are written in “if-then” form.
“If I study hard, then I will pass geometry”
What is the hypothesis?
What is the conclusion?
Ex) Re-write the following in “if-then” form:
• All monkeys have tails.
•
I will pass geometry by studying hard
•
Parallel lines do not intersect
The _________________ of a statement is the __________________ of the original statement.
Statement 1 The ball is red.
Statement 2 The cat is NOT black.
Negation 1 The ball is NOT red.
Negation 2 The cat is black.
Conditional statements can be true or false. To show a conditional statement is true, you must
prove that the conclusion is true every time the hypothesis is true. To show that a conditional
statement is false, you need to give only one counterexample.
Each conditional statement has a converse, an inverse, and a contrapositive statement.
• To write the converse, exchange the hypothesis and the conclusion
• To write the inverse, negate the hypothesis and the conclusion
• To write the contrapositive, first write the converse and then negate the hypothesis and
conclusion.
Ex) Write the if-then form, the converse, inverse, and contrapositive of the statement “Soccer
players are athletes”. Decide whether each statement is true or false.
Ex) Write the converse, inverse, and contrapositive of the following statement and decide which
are true or false: If two angles are vertical angles, then they are congruent.
You can write a definition as a conditional statement in if-then form or as its converse. Both the
conditional statement and its converse are true. For example, consider the definition of
perpendicular lines:
Perpendicular Lines
A __________________ _____________________ is a statement that contains the phrase “if
and only if”. Writing a biconditional statement is the equivalent to writing a conditional
statement AND its converse.
Ex) Two lines intersect if and only if they touch at exactly one point.
• Write the conditional statement:
•
Write the converse:
Ex) Consider the following statement:
x = 3 if and only if x^2 = 9.
Is this a biconditional statement?
Ex) Write the definition of a triangle in if-then form:
If a figure is a triangle, then _____________________________________________.
Write the converse of the definition:
Write the biconditional statement: