#tbt #4 Who Owns The Zebra?

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#tbt #4 Who Owns The Zebra? There are five different houses. Each house has its own color. Each house has a man of a different nationality. Each man drinks a different drink. Each man has a different pet. Each man drives a different car. The Englishmen lives in the red house. The Swede has a dog. The Dane drinks tea. The Green house is on the left side of the white house. The man in the green house drinks coffee. The man that drives a Ford has birds. The man in the yellow house drives a Chevy. The man in the middle house drinks milk. The Norwegian lives in the first house. The man that drives a Jeep lives in the house next to the house with cats. The man in the house next to the house with the horse, drives a Chevy. The man who drives an Audi drinks juice. The German drives a Nissan. The Norwegian lives next to the blue house. Water is drunk in the house next to the house where the Jeep belongs. Who owns the zebra? Can’t figure it out?? Take a picture and work on it at home  the German Einstein created this puzzle as a young boy

2.3 – Deductive Reasoning (day 2) September 18, 2014

Conditional Statement Symbolic notation Conditional Statement Converse p  q q  p Contrapositive Inverse ~q  ~p ~p  ~q

Laws of logic Law of Detachment Law of Syllogism Logical Argument: conclusion based on deductive reasoning. Deductive reasoning involves two laws: Law of Detachment Law of Syllogism

Law of detachment If p  q is a true conditional statement and p is true, then q is true. Ex: if two angles are vertical, then they are congruent. <ABC and <DBE are vertical angles So <ABC and <DBE are congruent. p  q p q

Law of detachment Example 2: (1) If you are a penguin, then you live in the Southern Hemisphere. (2) You are a penguin. Let p be the statement "you are a penguin", let q be the statement "you live in the Southern Hemisphere". Then (1) and (2) can be written If p, then q. p. So, by the Law of Detachment, we can deduce: q is true. That is, you live in the Southern Hemisphere.

Not the law of detachment The Law of Gossip… Michael knows that if he doesn’t do his chores in the morning, he won’t be allowed to play video games later on. Michael doesn’t play video games on Friday night. So Michael did not do his chores that morning. p  q q p

Law of syllogism An argument composed of two statements or premises, followed by a conclusion. If p  q and q  r are true conditional statements, then p  r is true.

Law of syllogism Example 1: (1) If it snows today, then I will wear my gloves. (2) If I wear my gloves, my fingers will get itchy. Let p be the statement "it snows today", let q be the statement "I wear my gloves", and let r be the statement "my fingers get itchy". Then (1) and (2) can be written If p, then q. If q, then r. So, by the Law of Syllogism, we can deduce: If p, then r. Or, if it snows today, my fingers will get itchy.

Just because something is a “valid argument” does not mean it is true! Validity vs. truth If the conclusion is guaranteed, the arguments is said to be valid. All dogs are horses. Fido is a dog. Therefore, Fido is a horse If the conclusion is not guaranteed (at least one instance in which the conclusion does not follow), the argument is said to be invalid. All dogs are mammals. Fido is a mammal. Therefore Fido is a dog Just because something is a “valid argument” does not mean it is true! Premises are supporting statements or argument. Ex 1: the conclusion follows the logic, even though it is unsound Ex 2

Examples: valid valid Valid, but certainly not true! All students eat pizza. Claire is a student at CSULB. Therefore, Claire eats pizza. All athletes work out in the gym. Barry Bonds is an athlete. Therefore, Barry Bonds works out in the gym. All math teachers are 7 feet tall Mrs. Pfeiffer is a math teacher Therefore, Mrs. Pfeiffer is 7 feet tall valid valid Valid, but certainly not true!

homework P. 92 # 30-42, 45-48 Make rough draft for “Create Your Own Conditional Statement”

Create your own conditional statement! Requirements: Create your own… Conditional statement Converse Inverse Contrapositive Biconditional Law of Detachment Law of Syllogism All based off your original conditional statement! Come up with a theme and a name for your theorem. Creativity counts!

Conditional statement If it is Saturday morning, then my husband is making breakfast.

Converse If my husband is making breakfast, then it is Saturday morning.

Inverse If it is not Saturday morning, then my husband is not making breakfast.

Contra-positive If my husband is not making breakfast, then it is not Saturday morning.

Biconditional It is Saturday morning, if and only if my husband is making breakfast.

Law of Detachment If it is Saturday morning, then my husband is making breakfast. It is Saturday morning, so my husband is making breakfast.

Law of syllogism If it is Saturday morning, then my husband is making breakfast. If my husband is making breakfast, then I’m sipping on coffee with my feet up relaxing. If its Saturday morning, then I’m sipping on coffee with my feet up relaxing.