Ch. 2 - Reasoning and Logic
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Ch. 2 - Reasoning and Logic Conditional Statements - Statements in "If, then" form PowerPoint PPT Presentation


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Ch. 2 - Reasoning and Logic Conditional Statements - Statements in "If, then" form The "If" is the hypothesis, and the "Then" is the conclusion. Ex: If a car is a Corvette, then it is a Chevrolet. p q Symbolic Representation: p q

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Ch. 2 - Reasoning and Logic Conditional Statements - Statements in "If, then" form

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Ch 2 reasoning and logic conditional statements statements in if then form

Ch. 2 - Reasoning and Logic

Conditional Statements - Statements in "If, then" form

The "If" is the hypothesis, and the "Then" is the conclusion.

Ex: If a car is a Corvette, then it is a Chevrolet.

p q

Symbolic Representation: p q

You read it like this:

q

If p, then q Or p implies q

q

p

q

hypothesis

conclusion


Ch 2 reasoning and logic conditional statements statements in if then form

Honda

Civic

Mrs. Stanley's car

Notice that the circle is completely inside the rectangle.

This indicates that ALL Civics are Hondas.

All Civics are Hondas. Mrs. Stanley drives a Civic.

Therefore, Mrs. Stanley drives a Honda.

This is an example of the Law of Detachment.


Ch 2 reasoning and logic conditional statements statements in if then form

Athletes

Basketball

Players

Football

Players

Both

Since both circles intersect, this implies that SOME athletes are 
BOTH football players and basketball players.


Ch 2 reasoning and logic conditional statements statements in if then form

Religion

Hinduism

Christianity

Since the circles do not intersect, this implies 
that NO Christians are Hindus and vice versa.


Ch 2 reasoning and logic conditional statements statements in if then form

Draw a Venn Diagram that represents the following statements.

1) All organic rocks are sedimentary.

2) Some organic rocks are coal. All coal is organic rock.

3) All chemical rocks are sedimentary. Chemical rocks are 
not organic.


Ch 2 reasoning and logic conditional statements statements in if then form

Example of Logic Statements:

Conditional

If a car is a Corvette, then it is a Chevrolet.

Converse (FLIP)

If a car is a Chevrolet, then is it a Corvette.

Inverse (NOT, negate)

If a car is NOT a Corvette, then it is NOT a Chevrolet.

Contrapositive (FLIP NOT)

If a car is NOT a Chevrolet, then it is NOT a Corvette.


Ch 2 reasoning and logic conditional statements statements in if then form

BICONDITIONAL STATEMENTS

If the conditional statement and the converse statement are both true, then they form a biconditional. We connect the hypothesis and conclusion with the words if and only if. (iff)

For example:

If an angle measures 90 degrees, then it is a right angle. TRUE

If an angle is a right angle, then its measure is 90 degrees. TRUE

Conclusion:

An angle measures 90 degrees if and only if it is a right angle.

The symbolic representation of iff is p q .


Ch 2 reasoning and logic conditional statements statements in if then form

Logical Chains - Conditional statements can be linked 
together like a chain

Remember the Transitive Property?

If a = b and if b = c, then a = c

(Notice that a and c are linked together by b.)

a b c

It is the same with conditional statements.

Given: If p then q, and if q then r.

Conclusion: If p then r. p q r

If p q, and if q r, then p r.


Ch 2 reasoning and logic conditional statements statements in if then form

The If-Then Transitive Property:

If p q, and if q r, and if r s, then p s.

Ex: When it's Tonya's night to cook, she always makes 
   hamburgers. p

q

When Tonya makes hamburgers, she burns them.

qr

If the hamburgers are burned, we order pizza.

rs

Therefore, when it's Tonya's night to cook, we order pizza.

ps

This is an example of the Law of Syllogism.


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