M4 Logic: Conditional Statements

M4 Logic: Conditional Statements

Statement

• A declarative sentence that is TRUE or FALSE but NOT BOTH

• sometimes called a "proposition"

Conditional Statement

• A way to decide whether a statement is true or false.

• If P then Q

•  $P\longrightarrow Q$  

• P is called the Hypothesis, Q is called the conclusion.

Conditional Statements example:

• "If it is not raining, then Daisy is riding her bike"

• Hypothesis will alway come after the word "IF".  Hypothesis = It is not raining.

• Conclusion will always come after the word "THEN".  Conclusion = Daisy is riding her bike.

Rewriting a statement in If then form

• You give me 1000 baht. I will be your best friend.

• Ans: If you give me 1000 baht, then I will be your best friend.

• Hypothesis: You give me 1000 baht. Conclusion: I will be your best friend.

Rewriting a statement in If then form

• I bring my umbrella when it is raining.

• Ans: If it is raining, then I will bring my umbrella.

• Hypothesis = It is raining. Conclusion = I will bring my umbrella

• This statement is in reverse. Think of what causes the situation.

• It is the rain that will cause me to bring the umbrella not if I bring my umbrella it will rain.

Multiple Choice

What is this?

• Conditional Statement
• Inverse
• Converse
• THIS IS A GEOMETRY CLASS!!! GIVE ME NUMBERS!

Multiple Select

What are the two parts of a conditional statement? (check 2 boxes)

• Hypothesis

• Conclusion

• Converse

• Inverse

Multiple Choice

p → q

• if p then q

• q then p

• not p

• not p then q

Multiple Choice

Given, "If angles are congruent, then the measures of the angles are equal." Identify the hypothesis.

• If angles are congruent.
• Angles are congruent.
• Then the measures of the angles are equal.
• The measures of the angles are equal.

Multiple Choice

Given, "If angles are congruent, then the measures of the angles are equal." Identify the conclusion.

• If the angles are congruent.
• The angles are congruent.
• Then the measures of the angles are equal.
• The measures of the angles are equal.

Multiple Choice

Given, "If I have a Siberian Husky, then I have a dog." Identify the hypothesis.

• If I have a Siberian Husky.
• I have a Siberian Husky.
• Then I have a dog.
• I have a dog.

Multiple Choice

Given, "If I have a Siberian Husky, then I have a dog." Identify the conclusion.

• If I have a Siberian Husky.
• I have a Siberian Husky.
• Then I have a dog.
• I have a dog.

Multiple Choice

Write the conclusion of the statement,

"If you are Anthony Rizzo, then you are a Chicago Cub."

• You are Anthony Rizzo.

• You are a Chicago Cub.

• The Cubs are the best.

Multiple Choice

Rewrite the statement as a conditional statement.

"All dolphins are mammals."

• If a dolphin, then a mammal.

• If an animal is a dolphin, then it is a mammal.

• If an animal is a mammal, then it is a dolphin.

• If an animal is not a mammal, then it is not a dolphin.

Multiple Choice

Rewrite the statement as a conditional statement.

"The sum of the angles of a triangle is 180."

• If the sum of the angles of a triangle, then 180.

• If a figure is a triangle, then the sum of the angles is 180.

• If a figure sums angles, then the triangle is 180.