Learning Chapter 2: Reasoning and Proof. Monday, September 21 st, 2015 Period 6

Learning Chapter 2: Reasoning and Proof Monday, September 21 st, 2015 Period 6

Learning Chapter 2 Objectives Identify and use symbols (~,, Ʌ, V,, ). Use and interpret Venn Diagrams to represent relationships. Create and identify the converse, inverse, contrapositive and biconditional of a conditional statement using words and symbols. Recognize and apply the Law of Detachment and the Law of Syllogism in both words and symbols. Identify and use adjacent, linear pair and vertical angles.

Identify and use symbols (~,, Ʌ, V,, ). -I understand the meanings of the symbols above. -I can translate verbal arguments into symbolic form. -I can translate symbolic representations into verbal meanings. Identificar y utilizar símbolos (~,, Ʌ, V,, ). -Comprender los significados de los símbolos anteriores. -Yo puedo traducir argumentos verbales en forma simbólica. -Yo puedo traducir las representaciones simbólicas en significados verbales. Learning Chapter 2a Goals

Fill in the meaning of each of the following symbols.

Example Given: p is likes to swim (p es me gusta nadar) q is go to the pool (q es ir a la piscine) Give the symbolic form of the sentences to the right. --> (Dar la forma simbólica de las oraciones a la derecha. -->) Symbolic Form: If you like to swim, then you go to the pool. (Si te gusta nadar, después ir a la piscina.) Brad does not go to the pool. (Brad no ir a la piscina.) Brad likes to swim and go to the pool. (Brad le gusta nadar e ir a la piscina.) Therefore, I like to swim. (Entonces, me gusta nadar.) I like to swim if and only if I go to the pool. (Me gusta nadar y sólo si voy a la piscina.)

(el control remoto no funciona) (la tele se convertirá) Qué es la representación simbólica de "si el control remoto está funcionando, entonces se enciende la tele."? Usar las opciones anteriores para completar las casillas de abajo.

Create and identify the converse, inverse, contrapositive and bi-conditional of a conditional statement using words and symbols. -I understand what a conditional statement is. -I can identify the hypothesis & conclusion within a conditional statement. -I can create and identify the converse, inverse, contrapositive, and biconditional from a conditional statement in words and in symbols. Crear e identificar las conversar, inversa, contrapositive y bi-condicional de una sentencia condicional utilizando palabras y símbolos. -Yo entiendo lo que es una sentencia condicional. -Yo puedo identificar las hipótesis y la conclusión en una sentencia condicional. -Yo Puedo crear e identificar el inverso, inverso, contrapositive y bicondicional de una instrucción condicional en palabras y en símbolos. Learning Chapter 2c Goals

TERM EASY MEANING SYMBOLS EXAMPLE Conditional Statement (condicional declaración) If Then If it is snowing, then we won t have school. (Si está nevando, entonces no tenemos escuela.) Hypothesis (hipótesis) Part after If Conclusion (conclusión) Part after Then

TERM EASY MEANING SYMBOLS EXAMPLE Converse (sustantivo) Switch or change order (Interruptor o cambio de orden) Inverse (inverso) Negate (add or remove the word not) (Negar (agregar o quitar la palabra no) Contrapositive Switch and negate (cambio y negate)

TERM EASY MEANING SYMBOLS EXAMPLE Biconditional If and only if (iff)

Identify the hypothesis and conclusion of this conditional statement: If two lines intersect at right angles, then the two lines are perpendicular.

Example 1: Write the converse, inverse, and contrapositive of this statement: Conditional If three points lie on the same line, then they are collinear. Converse (sustantivo): Inverse (inverso): Contrapositive: Which statement is equivalent to the original conditional statement? Qué afirmación es equivalente a la declaración condicional original?

Conditionals with Venn Diagrams If p, then q. P: Q P Q:

Conditionals with Venn Diagrams If it is snowing, then it is cold. P: Q:

Write the conditional statement illustrated by this Venn Diagram.

Write a conditional statement to represent the Venn Diagram. (Escriba una instrucción condicional para representar el diagrama de Venn.)

Draw a Venn Diagram to represent the conditional statement. (Dibujar un diagrama de Venn para representar la sentencia condicional.) If a shape is a square, then it is a quadrilateral.