Logic: LAW of DETACHMENT/LAW of SYLLOGISM

Logic: LAW OF DETACHMENT/LAW OF SYLLOGISM

Warm Up:

Rewrite the following statements as a conditional statement.

(1) An acute angle is an angle that measures less than 90 deg. and more than 0 deg.

(2) I am happy if I am fed.

(3) The car runs when there is gas in the tank.

Inductive Reasoning VER / SUS Deductive Reasoning

Law of Detachment(Direct Argument): If the ______of a ______conditional statement is true then the conclusion is also true.

Example 1: (1) If two segments have the same length then they are congruent.

(2) BC = XY

(3) Conclusion: ______

Example 2: (1) Every Friday and Saturday night Mary goes to the movies.

(2) Today is Friday.

(3) Conclusion: ______

Make your own!!!!

Try This #1

Assume the first sentence is true and then determine whether you can use the Law of Detachment with the 2nd sentence to make a conclusion. If a conclusion is possible then write it otherwise state no conclusion can be made.

(1) All students eat pizza. John is a student at LHS.

(2) All students at LHS work out in the gym. Kierenworks out in the gym.

(3) All math teachers love logic. Mr. Memory is a math teacher.

Law of Syllogism(Chain Rule):Syllogism works with the statements "If ______then ______" and "If ______then ______" (notice Q is mentioned twice). If both those statements are true, then the statement "If ______then ______" is true.

Example 3: (1) If Rick takes chemistry this year then Jesse will be Rick’s lab partner.

(2) If Jesse will be Rick’s lab partner then Rick will get an A in chemistry.

(3) Conclusion: ______

Example 4: (1) If I buy candy then I will spend money.

(2) If I go to the candy store then I will buy candy.

(3) Conclusion: ______

Make your own!!!!

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

(A) (1) If an angle measures more than 90 degrees then it is not acute.

(2) mABC = 120.

(3) Conclusion: ABC is not acute.

(B) (1) All 45 degree angles are congruent.

(2) AB

(3) Conclusion: A andB are 45 degree angles.

(2) Mathew ordered the apple pie.

(3) Conclusion: Mathew was served ice cream.

(D) (1) Ifa person wears school colors then he/she has school spirit.

(2) If a person has school spirit then the team feels great.

(3) Conclusion: If a personweasr the school colors then the team will feel great.

(E) (1) Ifsomeone eats too much turkey then he/she will get sick.

(2) Kinsley got sick.

(3) Conclusion: Kinsley ate too much turkey.

(F) (1) If2 is acute then 3 is obtuse.

(2) If 2 is not acute then 4 is a right angle.

(3) Conclusion: If 3 is not obtuse, then4 is a right angle.

(G) (1) If p then q.

(2) ~q

(3) Conclusion: ~p

TryThis #3: Assume the given statement is true. Then tell what you can conclude anything if each statement in a-d is also true. If no conclusion is possible say no conclusion.

(1) Given: If a person wins the lottery then he/she will be happy.

(A) John is happy. ______

(B) Phil is not happy. ______

(D) Jim does not win the lottery. ______

(2) All my students love geometry.

(A) John is my student. ______

(B) Otto loves geometry. ______

(D) Tom doesn’t love geometry. ______

(3) Create your own: ______

(A) Hypothesis: ______

(B) Conclusion: ______

(D) Conclusion Contrapositive ______

Try This #4: Use the Law of Syllogism to determine whether a valid conclusion can be reached from each set of statements. If a valid conclusion is possible write it.

(1)

(A) If two angles are complementary then the sum of their measures is 90.

(B) If the sum of the measures of two angles is 90, then both the angles are acute.

(2)

(A) If the heat wave continues then air conditioning will be used more frequently.

(B) If air conditioning is used more frequently then energy costs will be higher.

Extra Practice: Determine whether statement (3) follows from statement (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.

(A) (1) If it is Tuesday then Marla tutors chemistry.

(2) If Marla tutors chemistry then she arrives home at 4.

(3) If Marla arrives at home at 4 then it is Tuesday.

(B) (1) If a marine animal is a starfish then it lives in the intertidal zone of the ocean.

(2) The intertidal zone is the least stable of the ocean zones.

(3) If a marine animal is a starfish then it lives in the least stable of the ocean zones.