Standards - Mathematics

2019 - Mathematics Course of Study Document
Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.1

Represent logic statements in words, with symbols, and in truth tables, including conditional, biconditional, converse, inverse, contrapositive, and quantified statements.

Unpacked Content

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.

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

Aligned Learning Resources

Converse, Inverse, and Contrapositive of a Conditional Statement
Introduction to Truth Tables, Statements, and Logical Connectives
Truth Tables of Five Common Logical Connectives or Operators
16.1 And and Or Statements
16.4 Inverse, Converse, and Contrapositive
16.3 Negative Statements
16.2 If-Then Statements
Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.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

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.

Vocabulary

  • Compound statement
  • Negation
  • Conjunction
  • Disjunction

Aligned Learning Resources

Introduction to Truth Tables, Statements, and Logical Connectives
Truth Tables of Five Common Logical Connectives or Operators
16.1 And and Or Statements
16.4 Inverse, Converse, and Contrapositive
16.3 Negative Statements
16.2 If-Then Statements
Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.3

Use truth tables to solve application-based logic problems and determine the truth value of simple and compound statements including negations and implications.

Unpacked Content

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.

Vocabulary

  • Equivalent statements or logical equivalence

Aligned Learning Resources

16.3 Negative Statements
Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.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.

Unpacked Content

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.

Vocabulary

  • Tautology
  • Contradiction
  • Law of syllogism
  • Law of detachment/modus ponens

Aligned Learning Resources

16.3 Negative Statements
16.2 If-Then Statements
Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.5

Prove a statement indirectly by proving the contrapositive of the statement.

Unpacked Content

Knowledge

Students know:

  • A contrapositive is formed by negating both the hypothesis/antecedent and conclusion/consequent and reversing the direction of inference.
  • Proofs can be constructed by assuming that a hypothesis/antecedent is true and deducing that the conclusion/consequent is true.

Skills

Students are able to:

  • Write the contrapositive statement for a conditional statement such as a property of integers or other mathematical properties.
  • Construct a logical argument to prove a statement (such as a property of integers) is true by proving the contrapositive.

Understanding

Students understand that:

  • The contrapositive of a statement is logically equivalent to a statement.
  • A statement can be shown to be true by the laws of logic by proving that its contrapositive is true.

Vocabulary

  • Contrapositive
  • Proof by contrapositive
  • Indirect proof
  • hypothesis/antecedent
  • Conclusion/consequent

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