Which of the following is equivalent to A - B?
Understand the Problem
The question is asking which of the provided options is equivalent to the expression A - B, which is a set operation in mathematics. This involves understanding set theory concepts such as unions and intersections.
Answer
The equivalent expression to $A - B$ is $A \cap B'$.
Answer for screen readers
The expression equivalent to $A - B$ is $A \cap B'$.
Steps to Solve
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Understanding Set Difference The expression $A - B$ represents the set difference, meaning all elements in set $A$ that are not in set $B$. Mathematically, this can be expressed as $A \cap B'$, where $B'$ is the complement of set $B$.
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Translating the Expression Using the definition of set difference, we have: $$ A - B = A \cap B' $$ This means we need to find the equivalent expression among the options given.
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Analyzing the Options Evaluate the provided expressions:
- $A' \cup B$: This is not equivalent.
- $A \cap B'$: This matches our derived expression.
- $A \cup B'$: This does not match.
- $A' \cap B$: This is not equivalent.
- Identifying the Correct Option From the analysis, the expression that matches $A - B$ is: $$ A \cap B' $$
The expression equivalent to $A - B$ is $A \cap B'$.
More Information
The operation $A - B$ captures all elements that belong to set $A$ but not to set $B$. This is a fundamental concept in set theory, often used in various fields of mathematics and computer science.
Tips
- Confusing set difference with set intersection or union. Always remember that $A - B$ specifically excludes elements of $B$ from $A$.
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