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Conditional statements

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This document discusses conditional statements, their components, and logical equivalents. It provides an example of writing the converse, inverse, and contrapositive of the statement "If it has bacon then it is good." Additionally, it notes that the contrapositive of a conditional statement is logically equivalent and explains how a counterexample can disprove a statement.

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CONDITIONAL STATEMENTS Module 5 Lesson 6
THE STATEMENTS The original conditional statement is p -> q This is read as if p then q. p is the hypothesis and q is the conclusion Converse q->p Inverse ~p->~q. (~ means not) Contrapositive ~q->~p
LETS TRY ONE Use the following statement, write the converse, inverse and contrapositive. If it has bacon then it is good.
ANSWERS Converse: If it is good then it has bacon. Inverse: If it doesnt have bacon then it isnt good. Contrapositive: If it isnt good then it doesnt have bacon.
SOME THINGS YOU NEED TO KNOW If the conditional statement is true, then the contrapositive is true. If the conditional statement is false, then the contrapositive is false. A counterexample is something that disproves the statement.
NAME A COUNTEREXAMPLE If a shape is a quadrilateral then it is a square. If an animal swims then it is a duck. If it is February then it only has 28 days.
ANSWERS A rectangle is a quadrilateral but it isnt a square. A fish swims and it isnt a duck. Leap year

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Conditional statements

  • 2. THE STATEMENTS The original conditional statement is p -> q This is read as if p then q. p is the hypothesis and q is the conclusion Converse q->p Inverse ~p->~q. (~ means not) Contrapositive ~q->~p
  • 3. LETS TRY ONE Use the following statement, write the converse, inverse and contrapositive. If it has bacon then it is good.
  • 4. ANSWERS Converse: If it is good then it has bacon. Inverse: If it doesnt have bacon then it isnt good. Contrapositive: If it isnt good then it doesnt have bacon.
  • 5. SOME THINGS YOU NEED TO KNOW If the conditional statement is true, then the contrapositive is true. If the conditional statement is false, then the contrapositive is false. A counterexample is something that disproves the statement.
  • 6. NAME A COUNTEREXAMPLE If a shape is a quadrilateral then it is a square. If an animal swims then it is a duck. If it is February then it only has 28 days.
  • 7. ANSWERS A rectangle is a quadrilateral but it isnt a square. A fish swims and it isnt a duck. Leap year