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16.3 Negative Statements

Classroom Resource Information

Title:

16.3 Negative Statements

URL:

https://flexbooks.ck12.org/cbook/ck-12-precalculus-concepts-2.0/section/16.3/primary/lesson/negative-statements-pcalc/#

Content Source:

Other
CK-12

Type:

Informational Material

Overview:

This informational material will introduce negations and explain how to represent these logical statements with symbols in truth tables. It will introduce the term tautology and explain how a truth table can demonstrate a tautology. Practice questions with a PDF answer key are provided. In addition, there is a self-checking online practice tool.

Content Standard(s):

Mathematics MA2019 (2019) Grade: 9-12 Applications of Finite Math	1. Represent logic statements in words, with symbols, and in truth tables, including conditional, biconditional, converse, inverse, contrapositive, and quantified statements. Unpacked Content Evidence Of Student Attainment: Students: Represent propositional statements using statement variables and logical operators. Construct a truth table for a statement. Construct conditional, biconditional, converse, inverse contrapositive, and quantified statements. Teacher Vocabulary: Proposition Statement variables Logical operators Truth table Negation Conditional statement Hypothesis/antecedent Conclusion/consequent Converse statement Inverse statement Contrapositive statement Biconditional statement Equivalent statements Knowledge: Students know: How to determine if a simple statement is true or false. Skills: Students are able to: Construct a truth table for propositions with a variety of operators. Write a proposition using logical operators and statement variables such as p and q. Write the converse, inverse, contrapositive and biconditional of a conditional statement using logical operators and statement variables. Understanding: Students understand that: A conditional statement's validity is based on the validity of its components. Truth tables must contain all possible assignments of true and false for each component. A statement is either true or false. Diverse Learning Needs:
Mathematics MA2019 (2019) Grade: 9-12 Applications of Finite Math	2. Represent logic operations such as and, or, not, nor, and x or (exclusive or) in words, with symbols, and in truth tables. Unpacked Content Evidence Of Student Attainment: Students: Determine the appropriate logical operators needed to write a compound statement with symbols and statement variables. Determine the truth value for each component of a compound statement and organize in a truth table. Teacher Vocabulary: Compound statement Negation Conjunction Disjunction Knowledge: Students know: A statement is either true or false. A truth table must include every possible assignment of true and false for each component of a compound statement. Skills: Students are able to: Construct a truth table for a compound statement. Represent compound statements using statement variables and logical operators. Understanding: Students understand that: The validity of the simple statements that make up a compound statement determine the compound statement's validity. Diverse Learning Needs:
Mathematics MA2019 (2019) Grade: 9-12 Applications of Finite Math	3. Use truth tables to solve application-based logic problems and determine the truth value of simple and compound statements including negations and implications. a. Determine whether statements are equivalent and construct equivalent statements. Example: Show that the contrapositive of a statement is its logical equivalent. Unpacked Content Evidence Of Student Attainment: Students: Solve an application-based logic problem using a truth table. Recognize when two statements have the same truth value. Teacher Vocabulary: Equivalent statements or logical equivalence Knowledge: Students know: How to construct a truth table from a given logic statement. Skills: Students are able to: Represent an application-based logic problem as a statement(s) using logical operators and statement variables. Construct a truth table to determine a solution to a logic problem. Understanding: Students understand that: Complex situations including logic problems can be modeled using truth tables. Statements are logically equivalent if they have the same truth value for every possible assignment of true and false for each component. Diverse Learning Needs:
Mathematics MA2019 (2019) Grade: 9-12 Applications of Finite Math	4. Determine whether a logical argument is valid or invalid, using laws of logic such as the law of syllogism and the law of detachment. a. Determine whether a logical argument is a tautology or a contradiction. Unpacked Content Evidence Of Student Attainment: Students: Recognize if an argument is valid. Teacher Vocabulary: Tautology Contradiction Law of syllogism Law of detachment/modus ponens Knowledge: Students know: How to construct a truth table from a given logic statement. Skills: Students are able to: Construct valid arguments. Identify the validity of arguments. Understanding: Students understand that: Truth tables can be used to construct a valid argument or to determine the validity of an argument. In order for an argument to be valid, the form of the argument must be valid. Diverse Learning Needs:

Tags:

and, conditional, conjunction, disjunction, logic statement, negation, or, symbol, tautology, truth table

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Author:

Hannah Bradley

ALEX Classroom Resource

16.3 Negative Statements