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. C ⊆ U

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Recall that the symbol ⊆ means 'is a subset of,' which means every element of set C must also be an element of set U.

List the elements of set C: {4, 10, 12}.

List the elements of set U: {2, 4, 6, 8, 10, 12, 14}.

Check each element of C to see if it is in U: 4 is in U, 10 is in U, and 12 is in U.

Since all elements of C are found in U, conclude that C ⊆ U is true.

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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 B if every element of A is also an element of B. This means all members of A must be contained within B for A ⊆ B 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 one set is present in another.

Universal Set

The universal set U contains all elements under consideration in a given context. Subsets are always compared to the universal set or other sets within it.

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