Conditional Statements

Conditional Statements

Logic and Conditional Statements

• Conditional Statement:

   $p\ \rightarrow\ q$  which means "if p then q"

• Hypothesis and Conclulsion

• Counter-example

• Negation

• Converse , Inverse, Contrapositive

Multiple Choice

Rewrite the following conditional statement in if-then form: "All numbers divisible by 4 are also divisible by 2"

• If a number is divisible by 4 then it is divisible by 2

• If a number is divisible by 2 then it is divisible by 4

• If a number is not divisible by 4 then it is divisible by 2

• If there is a 4 then there is a 2

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.

Counter-Example Examples

Preserves the Hypothesis but contradicts the Conclusion

Multiple Choice

If false, which is a counterexample?

• It's True

• My clothes are dry

• I jumped in a pool

• It is raining

Multiple Choice

If false, which is a counterexample?

• It's True

• $\angle E$ is obtuse

Multiple Choice

If false, which is a counterexample?

• It's True

• 6

• 12

• 8

Negation

The opposite of a statement.

 $\sim$  is the symbol for 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

Multiple Choice

What is the Negation of the inequality:  $x\ge6$ ?

•  $x<6$  

•  $x\le6$  
  

•  $x>6$  
  

•  $x\ge6$  
  

Rearranging Conditionals

• Converse

• Inverse

• Contrapositive

Complete the three examples shown...