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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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.
Symbolic Representation: p q
You read it like this:
If p, then q Or p implies q
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.
Since both circles intersect, this implies that SOME athletes are BOTH football players and basketball players.
Since the circles do not intersect, this implies that NO Christians are Hindus and vice versa.
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: statements.
If a car is a Corvette, then it is a Chevrolet.
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 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)
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
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: together like a chain
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
When Tonya makes hamburgers, she burns them.
If the hamburgers are burned, we order pizza.
Therefore, when it's Tonya's night to cook, we order pizza.
This is an example of the Law of Syllogism.