Conditional Statements/ Intro to Proofs

If it is Valentine's Day, then the month is February. What is the hypothesis (p) of this statement?

• it is not Valentine's Day

• it is Valentine's Day

• the month is not February

• the month is February

What is the Inverse ( ∼p→∼q )  of the statement: If I go to the cafeteria, then I get lunch.

• If I get lunch, then I go to the cafeteria.

• If I do not get lunch, then I do not go to the cafeteria.

• If I do not go to the cafeteria, then I do not get lunch.

• If I do not get lunch, then I do not go to the cafeteria.

What is the converse ( q→p  ) of the statement:

If you are 13, then you are a teenager.

• If you are not 13, then you are a teenager.

• If you are 13, then you are not a teenager.

  
  

• If you are a teenager, then you are 13.

• If you are not a teenager, then you are not 13.

What is the conclusion (q) of the statement:

If two angles are congruent, then they have the same degree.

• they have the same degree.

• two angles are congruent

• 
  two angles are not congruent

• they do not have the same degree.

What is the contrapositive (∼q→∼p  ) of the statement:

If you play the guitar, then you are a musician.

• If you are a musician, then you play the guitar.

• If you are not a musician, then you do not play the guitar.

• If you do not play the guitar, then you are not a musician.

• If you play the guitar, then you are a musician.

What is the inverse ( ∼p→∼q  ) of the statement:

If you play the guitar, then you are a musician.

• If you are a musician, then you play the guitar.

• If you are not a musician, then you do not play the guitar.

• If you do not play the guitar, then you are not a musician.

• If you play the guitar, then you are a musician.

What is the negation of the hypothesis (~p) of the statement:

If two angles are congruent, then they have the same degree.

• they have the same degree.

• two angles are congruent

• two angles are not congruent

• they do not have the same degree.

What is the contrapositive ( ∼q→∼p  ) of the statement:

If you are 13, then you are a teenager.

• If you are not 13, then you are a teenager.

• If you are 13, then you are not a teenager.

• If you are a teenager, then you are 13.

• If you are not a teenager, then you are not 13.

What is the negation of the conclusion (~q) of this statement?

If it is Valentine's Day, then the month is February.

• it is not Valentine's Day

• it is Valentine's Day

• the month is not February

• the month is February

What is the negation of the hypothesis (~p) of this statement?

If it is Valentine's Day, then the month is February.

• it is not Valentine's Day

• it is Valentine's Day

• the month is not February

• the month is February