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Conditional Statements and Logic Chains

Conditional Statements and Logic Chains. Conditional Statements. two parts – hypothesis and conclusion Usually written in if- then form The “if” part is the hypothesis The “then” part is the conclusion. Counterexamples. A counterexample can be written to prove a conditional false

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Conditional Statements and Logic Chains

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  1. Conditional Statements and Logic Chains

  2. Conditional Statements • two parts – hypothesis and conclusion • Usually written in if- then form • The “if” part is the hypothesis • The “then” part is the conclusion

  3. Counterexamples • A counterexample can be written to prove a conditional false • Only ONE counterexample is needed. Instances • An instance is an example of a conditional

  4. Example: Tell whether each is an instance, counterexample, or neither. If angle A is acute, then it measures 25° • m<A = 25° • m<A = 37° • m<A = 95°

  5. Converse • Formed by switching the hypothesis and conclusion of a conditional • Switch the “if” and “then” • Example: Write the converse of the conditional. If you trip over a desk, then you will fall.

  6. Inverse • Formed by negating the hypothesis and conclusion of a conditional • “if not” and “then not” • Example: Write the inverseof the conditional. If you trip over a desk, then you will fall.

  7. Contrapositive • Formed by switching and negating the hypothesis and conclusion of a conditional • Switch the “if not ” and “then not” • Example: Write the contrapositiveof the conditional. If you trip over a desk, then you will fall.

  8. Euler Diagrampronounced “Oiler” Diagram • Often called Venn Diagrams • Can be drawn to represent the conditional “Then” “If”

  9. Example: Draw an Euler Diagram for the following conditional: If you are 16 years old, then you can drive a car. People who can drive a car 16 year olds

  10. Biconditionals • conditionals whose statements can be interpreted “forward” or “backward”; the conditional and its converse are true • Written as an “if and only if” statement • Example: write a biconditional for the conditional: If an angle measures 90°, then it is a right angle.

  11. Logic Chains • a logic chain is a series of conditionals that can be put together to form a logical conclusion. • Example: If cats freak, then mice frisk. If sirens shriek, then dogs howl. If dogs howl, then cats freak. Use these statements to logically show: If sirens shriek, then mice frisk.

  12. Constructing Logic Chains Row Races Organize each logic chain and give the conclusion that follows. Person 1 write 1st conditional, Person 2, 2nd, and so on. The final person will write the conclusion.

  13. If it is cold, then the birds fly south. If the days are short, then it is cold. If it is winter, then the days are short.

  14. If the police catch Tim speeding, then Tim gets a ticket. • If Tim drives a car, then Tim drives too fast. • If Tim drives too fast, then the police catch Tim speeding.

  15. If quompiesplaun, then romplesgleer. • If ruskersbleer, then homblersfrain. • If homblersfrain, then quompiesplaun.

  16. If you go to a movie, then you will spend all of your money. • If you clean your room, then you will go to a movie. • If you cannot buy gas for the car, then you will be stranded. • If you spend all of your money, then you cannot buy gas for the car.

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