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 ⊆ C

Key Concepts

Set Theory

Set theory is a branch of mathematical logic that studies sets, which are collections of objects. In this context, understanding the relationships between sets, such as subsets, unions, and intersections, is crucial. A set A is a subset of set C (denoted A ⊆ C) if every element of A is also an element of C.

Subset Definition

A subset is a set whose elements are all contained within another set. For example, if A = {2, 4, 6} and B = {2, 4, 6, 8}, then A is a subset of B. To determine if A ⊆ C, we must check if all elements of A are present in C, which requires a direct comparison of the elements in both sets.

Element Comparison

Element comparison involves checking whether specific elements of one set exist in another set. In this problem, we need to compare the elements of set A with those of set C. If any element of A is not found in C, then the statement A ⊆ C is false, highlighting the importance of thorough examination of each element.