In Exercises 1–6, find the intersection of the sets.{ a, b, c, d} ⋂ ∅

Verified step by step guidance

1. Identify the two sets involved in the intersection: Set A = \{ a, b, c, d \} and the empty set \( \emptyset \).
2. Recall the definition of intersection: The intersection of two sets is a new set containing all elements that are common to both sets.
3. Consider the empty set \( \emptyset \): It contains no elements.
4. Determine the common elements between Set A and the empty set: Since the empty set has no elements, there are no common elements.
5. Conclude that the intersection of Set A and the empty set is the empty set \( \emptyset \).

Key Concepts

Sets

A set is a collection of distinct objects, considered as an object in its own right. Sets can contain numbers, letters, or other sets, and are typically denoted by curly braces. Understanding sets is fundamental in mathematics, as they form the basis for various operations and relations.

Intersection of Sets

The intersection of two sets is a new set that contains all the elements that are common to both sets. It is denoted by the symbol '∩'. For example, if set A contains {a, b, c} and set B contains {b, c, d}, then the intersection A ∩ B would be {b, c}.

Empty Set

The empty set, denoted by '∅', is a set that contains no elements. It is a fundamental concept in set theory, representing the idea of 'nothing' in a mathematical context. The intersection of any set with the empty set is always the empty set, as there are no common elements.