Truth Tables of Five Common Logical Connectives or Operators

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

This material will construct the five common logical connectives or operators. They are considered common logical connectives because they are very popular, useful, and always taught together.

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.

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.

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.

Resource Provider

Other

License Type

CUSTOM

Resource Provider other

ChiliMath
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