Sec 2-3

Concept: Deductive ReasoningObjective: Given a statement, use the laws of logic to form conclusions and determine if the statement is true through completion of daily work

Example 1: Use the true statements to determine whether the conclusion is true or false. Explain your reasoning

If Diego goes shopping, then he will buy a pretzel If the mall is open, then Angela and Diego will go

shopping If Angela goes shopping, then she will buy a pizza The mall is open

a. Diego bought a pretzelTRUE!

Since the mall is open, Angela and Diego go shopping and

therefore, Diego buys a pretzel

Example 1 cont.: Use the true statements to determine whether the conclusion is true or false. Explain your reasoning

If Diego goes shopping, then he will buy a pretzel If the mall is open, then Angela and Diego will go

shopping If Angela goes shopping, then she will buy a pizza The mall is open

b. Angela and Diego went shoppingTRUE!

Since the mall is open, Angela and Diego went shopping

Example 1 cont.: Use the true statements to determine whether the conclusion is true or false. Explain your reasoning

If Diego goes shopping, then he will buy a pretzel If the mall is open, then Angela and Diego will go

shopping If Angela goes shopping, then she will buy a pizza The mall is open

c. Angela bought a pretzelFALSE!

Since the mall is open, Angela and Diego went shopping,

therefore, Angela bought a pizza

Example 1: Use the true statements to determine whether the conclusion is true or false. Explain your reasoning

If Diego goes shopping, then he will buy a pretzel If the mall is open, then Angela and Diego will go

shopping If Angela goes shopping, then she will buy a pizza The mall is open

d. Diego had some of Angela’s PizzaFALSE!

Since the mall is open, Angela and Diego went shopping, therefore, Diego bought a

pretzel

Example 2: Deductive Reasoning

A.

B.

Example 3: Write the symbolic statement in words.

p: the sky is cloudy q: it is raining

1. ~p The sky is not cloudy

2. ~q It is not raining

3. p→q If the sky is cloudy, then it is raining

If the sky is not cloudy, then it is not raining.If it is raining, then the sky is cloudy

4. ~p→~q

5. q→p

6. ~q→~p If it is not raining, then the sky is not cloudy

7. p↔q The sky is cloudy if and only if it is raining.

Example 4: Determine if statement (3) follows from statements (1) and (2) by the Law of Detachment or the Law of Syllogism. If it does, state which law was used. If it does not, write invalid.

(1)If you are a teenager, then you are always right

(2)If you are always right, then people will listen to you

(3)If you are a teenager, then people will listen to you

Law of Detachment:

If p→q is a true conditional statement and p is true, then q is true

Law of Syllogism:

If p→q and q→r, then p→r

p qq rp r

LAW OF SYLLOGISM

Example 4 Continued: Determine if statement (3) follows from statements (1) and (2) by the Law of Detachment or the Law of Syllogism. If it does, state which law was used.

(1)If an angle is acute, then it is not obtuse

(2)<ABC is actue

(3)<ABC is not obtuse

Law of Detachment:

If p→q is a true conditional statement and p is true, then q is true

Law of Syllogism:

If p→q and q→r, then q→r

p qp: true

q: must be truetrue

Law of Detachment

Today’s Work