Education Technology

Closure Tables

Activity Overview

In this activity, students create and complete closure tables to determine if the sets of whole numbers, integers, even numbers, and odd numbers are closed under the operations of addition, subtraction, multiplication, and division.

Key Steps

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    Closure tables are a way to organize your work when checking to see if sets are closed under operations. The closure table for {0, 1} under multiplication is shown.
    Closure tables are similar to multiplication tables, but they can show any operation. To read them, find a number in the first column and a number in the first row. The intersection of these gives the result of the two numbers under that operation.
    To use the closure table to determine if this set is closed under multiplication, look at each of the products in the table. All of the products belong to the set {0, 1} so this set is closed under multiplication.