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### Conditional Statements and Laws

Logic Lesson 1

Do Now

7. Y is the midpoint of XZ. If XY measures x – 2, and XZ measures 3x – 16, what is the measure of YZ?

8. Find the measure of ∠CAB.

Conditional Statements Notes

If an object is red, then that object is an apple.

If hypothesis, thenconclusion.

If an object is an apple, then that object is red.

If an object is not red, then that object is not an apple.

If an object is not an apple, then that object is not red.

Conditional Statements Notes

You can provide a counterexample to prove statements are false.

For a counterexample, the hypothesis must be true and the conclusion must be false!

If an animal is a duck, then that animal has wings.

If an animal has wings, then that animal is a duck.

If an animal is not a duck, then that animal does not have wings.

If an animal does not have wings, then that animal is not a duck.

Biconditional Notes

A biconditional statement occurs when a conditional and its converse are both true.

These can be joined with “if and only if”.

Example: An angle is a right angle if and only if it measures 90°.

Law of Detachment Notes

If a conditional statement is true and you have a “detached” 2nd statement, you can conclude that it is true as well.

Example: If an animal is a dog then it has a tail.

Tank is a dog…

therefore, Tank has a tail.

Law of Syllogism Notes

If you have two conditionals that are both true, a conditional that relates the 1st and the 3rd statement is also true.

Example: If I do my homework I will get good grades.

If I get good grades my parents will buy me a car.

Therefore, if I do my homework…

my parents will buy me a car.

Class Example 1

Identify the hypothesis and conclusion.

You will make the honor roll if you get all A’s and B’s.

Class Example 2

Provide a counterexample to show that the conditional statement is false.

If a number is odd, then it is a prime number.

Class Example 3

Write the inverse of the statement. Is it true or false? If false provide a counterexample.

If a bird is a raven then it is black.

Class Example 4

Write the converse of the statement and decide if the original statement is a biconditional. If it is, write the statement as a biconditional, if not give a counterexample.

If something is an airplane then it can fly.

Student Example 2

Write the converse of the statement.

If a number is divisible by 6 then it is divisible by 3.

Student Example 3

Write two conditional statements that make up the following biconditional.

I wear boots if and only if it is raining.

Student Example 5

Draw a conclusion. State if you used the Law of Syllogism or the Law of Detachment.

If A then B. If B then C. A therefore…

Logic Classwork

You are going to write and illustrate one conditional statement along with its converse, inverse, and contrapositive.

You can use any conditional statement.

If you can’t think of one, you can select from this list:

If you graduate high school then you’ll get a new car.

If you have red hair then you are smart.

If you get scared then you pee your pants.

If you eat carrots then you’ll have good eyesight.

If you pick your nose then you will go to prom alone.

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