Let A = {2, 4, 6, 8, 10, 12}, B = {2, 4, 8, 10}, C = {4, 10, 12}, D = {2, 10}, andU = {2, 4, 6, 8, 10, 12, 14}. Determine whether each statement is true or false. A ⊆ U

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Identify the sets given: $ A = \{2, 4, 6, 8, 10, 12\} $ and $ U = \{2, 4, 6, 8, 10, 12, 14\} $.

Recall the definition of subset: $ A \subseteq U $ means every element of $ A $ is also an element of $ U $.

Check each element of $ A $ to see if it is contained in $ U $: verify if 2, 4, 6, 8, 10, and 12 are all in $ U $.

Since all elements of $ A $ appear in $ U $, conclude that $ A \subseteq U $ is true.

If any element of $ A $ was not in $ U $, then $ A \subseteq U $ would be false.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Subset Definition

A set A is a subset of set U if every element of A is also an element of U. This means all members of A must be contained within U for A ⊆ U to be true.

Set Membership

Set membership refers to whether an element belongs to a particular set. To verify subset relations, you check if each element of the first set is a member of the second set.

Universal Set

The universal set U contains all elements under consideration in a particular context. Subsets are always compared to this universal set to determine inclusion or exclusion.

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