2.1 Conditional Statements with work
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Sep 2111:17 AM
2.1 Conditional Statements
Conditional: A statement that can be written in “ifthen” format. Also
often noted as , which can be read as ”.
Hypothesis: The part of a conditional statement following the “if.”
Conclusion: The part of a conditional statement following the “then.”
Rewrite the following statements in conditional “ifthen” form.5. Acute angles are less than 90 degrees.
6. The game will be played provided it doesn’t rain.
7. All runners are athletes.
Sep 2111:17 AM
Given a conditional in the form , there are three variations onthe conditional.
Conditional:
Converse: Notice that the hypothesis and the conclusion areswitched.
Inverse: This statement reads “if not p then not q”. Thehypothesis and conclusion of the original conditional statement have be “negated”.
Contrapositive Reads “if not q then not p”. This is the negationof the converse statement.
Sep 2111:18 AM
Definitions:Truth Value: The truthfulness or falseness of a conditional statement, its converse, its inverse, and its contrapositive.
Logically Equivalent: When statements have the same truth value. (either true or false).
Counterexample: A specific situation or example used to disprove a statement
BiConditional: Exists when a conditional and its converse are both true. BiConditionals can be written in a special formal using the notation “iff” which stands for “if and only if.”Note: All Definitions are BiConditionals
Sep 2111:19 AM
Examples:Conditional: If a candy bar is a Milky Way, then it contains caramel. (True)
All Milky Ways contain Caramel!Converse: If a candy bar contains caramel, then it is a Milky Way. (False)
A Snickers contains caramel but it isn’t a Milky Way!
Inverse: If a candy bar is not a Milky Way, then it does not contain caramel. (False) Again, a Snickers would be a counterexample to the statement.
Contrapositive: If a candy bar does not contain caramel, then it is not a Milky Way. (True) If a candy bar doesn’t contain any caramel then we know for sure it is not a Milky Way!
Write the converse, inverse, contrapositive for the conditional given and assess the truth value for each statement.
Conditional: If you are a teenager, then you are 13. (False)
Converse: ________________________________________________________________ ( )Inverse: __________________________________________________________________ ( )Contrapositive: _____________________________________________________________ ( )
Sep 2111:20 AM
Conditional: If an angle is a right angle, then it measures 90 degrees. (True)Converse: _________________________________________________________________( )Inverse: ___________________________________________________________________( )Contrapositive: _____________________________________________________________ ( )
Conditional: If then . (True)
Converse: ____________________________ ( )Inverse: ______________________________ ( )Contrapositive: ________________________ ( )
Do you notice a pattern between the truth values of the statements? _______________________________________________________________________________
Sep 2111:22 AM
Biconditional Examples:
Write two conditionals that are equivalent to the given biconditional.An angle is a right angle if and only if its measure is 90 degrees.
Given the following conditional and its converse, rewrite the statements as a biconditional.Conditional: If two angles have the same measure, then they are congruent.Converse: If two angles are congruent, then they have the same measure.
Determine which of the following statements are biconditionals._____All runners are athletic._____A triangle is a polygon with three sides._____Angles greater than 90 degrees are obtuse._____Integers are numbers_____Congruent segments are equal in measure.
A definition is a “good” definition only if it can be written as a biconditional. Determine whether the following are “good” or “bad” definitions.
Pear: a fruit which can be eatenEquilateral Triangle: a triangle in which all three sides are of equal lengthSquare: a polygon with exactly four sidesTeacher: a person who works for the public schoolsPerpendicular Lines: two lines which intersect to form right angles
2.1 Conditional Statements with work
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Sep 2612:26 PM
Venn DiagramsAlways
Sometimes
Never
if...
then...
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