Learning Resource Type

Classroom Resource

16.4 Inverse, Converse, and Contrapositive

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

This informational material will introduce students to inverse, converse, and contrapositive logic statements. The use of symbols and truth tables for these logical statements is explained. There is a corresponding video available. Practice questions with a PDF answer key are provided. In addition, there is a self-checking online practice tool.

    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

    UP:MA19.FM.1

    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.

    Body

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

    UP:MA19.FM.2

    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.

    Body

    1. Represent logic operations such as and, or, not, nor, and x or (exclusive or) in words, with symbols, and in truth tables.
    Link to Resource

    CR Resource Type

    Informational Material

    Resource Provider

    CK-12
    Accessibility
    License

    License Type

    Custom
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