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

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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

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

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.

Athletes

Basketball

Players

Football

Players

Both

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

Religion

Hinduism

Christianity

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

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.

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.

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 .

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.

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.