Problem 27 - College Algebra Essentials

Question

Find the intersection of the sets. $$\\{a, b, c, d\\} \cap \varnothing$$

Step-by-Step Solution

Answer

The intersection of the sets \({a, b, c, d}\) and \(\varnothing\) is \(\varnothing\) (an empty set) as there are no common elements between the two sets.

Step 1: Understanding the concept of Intersection

The intersections of two sets A and B, denoted as \(A \cap B\), is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements. It comprises the common elements from both sets.

Step 2: Identify common elements

The given sets are \({a, b, c, d}\) and \(\varnothing\) (an empty set). The empty set does not contain any elements. Therefore, there are no common elements between the set \({a, b, c, d}\) and the empty set.

Step 3: Declare the Intersection

Since there are no common elements between \({a, b, c, d}\) and \(\varnothing\), the intersection of these sets is itself an empty set: \(\varnothing\).