1. Intro to Conditional Statements

Conditional Statements

Lesson

A Conditional Statement is a statement that can be written in
IF-THEN form. 

Symbolic Form: p→q 

(read as “if p, then q” or “p implies q”)

Multiple Choice

What symbolic form of a conditional statement mean 'If $$p$$  then $$q$$ ?

• $$p\rightarrow q$$  

• $$q\rightarrow p$$  

• $$\sim q\rightarrow\sim p$$  

• $$\sim p\rightarrow\sim q$$  

Hypothesis and Conclusion of a Conditional

• Hypothesis follows the 'if'

• Conclusion follows the 'then'

Multiple Choice

What is the hypothesis of the conditional?

• You are an American citizen.

• You have the right to vote.

• You are not an American citizen.

• You do not have the right to vote.

Multiple Choice

What is the Conclusion of the conditional?

• You are an American citizen.

• You have the right to vote.

• You are not an American citizen.

• You do not have the right to vote.

Negation

Multiple Choice

Which stands for "if not p then q" ?

• $$\sim p\rightarrow q$$

• $$\sim p\rightarrow\sim q$$

• $$p\rightarrow q$$

• $$p\rightarrow\sim q$$

Multiple Choice

What is the Negation of the statement: 'I went to the store' ?

• I did not go to the store

• I went to Shaws

• I did not leave the house

• I went home

Logically equivalent means they are both true

Converse: Formed by switching the hypothesis and conclusion.

• Symbolic Form: q→p

Multiple Choice

Which of the following is the CONVERSE of the statement below?

If an object is a ring, then it is

made of gold.

• If an object is made of gold, then it is a ring.

• If an object is not a ring, then it is not made of god.

• If an object is not made of gold, then it is not a ring.

• There is no converse of the statement.

Multiple Choice

Which of the following is the CONVERSE of the statement below?

If an object is a bird, then it can fly.

• If an object can fly, then it is a bird.

• If an object is not a bird, then it cannot fly

• If an object cannot fly, then it is not a bird

• There is no converse of the statement

Inverse

Multiple Choice

Select the inverse of the following conditional statement:

If I study for the test, then I will get a good grade.

• If I don't study for the test, then I will not get a good grade.

• If I did not get a good grade, then I did not study for the test.

• If I get a good grade, then I studied for the test.

Multiple Choice

Which of the following is the symbolic notation for an inverse statement?

• p→q

• p↔q

• ~p→ ~q

• q→p

Contrapositive

Conditional Statement: If you are a yellow sponge, then you are SpongeBob Square Pants.

Contrapositive: If you are not SpongeBob Square Pants, then you are not a yellow sponge.

Multiple Choice

Select the contrapositive of the following conditional statement.

If I study for the test, then I will get a good grade.

• If I don't study for the test, then I will not get a good grade.

• If I get a good grade, then I studied for the test.

• If I did not get a good grade, then I did not study for the test.

Multiple Choice

Which of the following is the symbolic notation for a contrapositive statement.

• $$p\rightarrow q$$  

• $$p\leftrightarrow q$$  

• $$\sim p\rightarrow\ \sim q$$  

• $$\sim q\rightarrow\sim p$$  

Conditional Statement: If p, then q.

If you live in MD, then you live in the USA.

• Converse (if q, then p): If you live in the USA, then you live in MD.

• Inverse (if not p, then not q): If you do not live in MD, then you do not live in the USA.

• Contrapositive (if not q, then not p): If you do not live in the USA, then you do not live in MD.

Match

Page 3 #1

If an angle is 145 degrees, then it is an obtuse angle.

• a. Hypothesis

• b. Conclusion

• c. Inverse

• d. Converse

• e. Contrapositive

An angle is 145 degrees

It is obtuse

If angle is not 145,then it's not obtuse

If it is obtuse, then angle is 145

If it's not obtuse,then angle is not 145

• An angle is 145 degrees

• It is obtuse

• If angle is not 145,then it's not obtuse

• If it is obtuse, then angle is 145

• If it's not obtuse,then angle is not 145

Multiple Choice

What is the conclusion to the statement?

• You like fried chicken
• You only like fried chicken from KFC
• You like KFC
• You hate KFC

Multiple Choice

What is the hypothesis of this conditional?

• Sally goes to the park.
• Sally will fall off the swing.
• Parks don't have swings that Sally goes to.
• If Sally falls off the swing, she goes to the park.

Multiple Choice

Original: If Emily is not late to class, then she will not be marked tardy.
What is this? If Emily is late to class, then she will be marked tardy.

• Converse
• Inverse
• Contrapositive
• Negation

Multiple Choice

Conditional: If it does not rain today, then we will have practice.
What is this statement called: If it rains today, then we will not have practice.

• Converse
• Inverse
• Contrapositive
• Negation

Multiple Choice

What is the contrapositive of the following statement?
If it is Saturday, then the school is closed

• If the school is closed, then it is Saturday.
• If it is not Saturday, then the school is not closed.
• If the school is not closed, then it is not Saturday.

Multiple Choice

What is the converse of the following statement?
If it is Saturday, then the school is closed

• If the school is closed, then it is Saturday.
• If it is not Saturday, then the school is not closed.
• If the school is not closed, then it is not Saturday.