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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 hypothesisconclusion pq

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Civic Mrs. Stanley's car Honda 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.

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Athletes Football Players Basketball Players Since both circles intersect, this implies that SOME athletes are BOTH football players and basketball players. Both

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

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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.

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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. Example of Logic Statements:

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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. BICONDITIONAL STATEMENTS

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Logical Chains - Conditional statements can be linked together like a chain R emember 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. G iven: 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.

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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. q r If the hamburgers are burned, we order pizza. r s Therefore, when it's Tonya's night to cook, we order pizza. p s This is an example of the Law of Syllogism.

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Section 3.3 Using Laws of Logic. Using contrapositives The negation of a hypothesis or of a conclusion is formed by denying the original hypothesis.

Section 3.3 Using Laws of Logic. Using contrapositives The negation of a hypothesis or of a conclusion is formed by denying the original hypothesis.

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