Question

Suppose $A, B$, and $C$ are events in some sample space $\Omega$, and thus are subsets of $\Omega$. Prove the distributive law $$ (A \cup B) \cap C=(A \cap C) \cup(B \cap C) . $$

   Suppose $A, B$, and $C$ are events in some sample space $\Omega$, and thus are subsets of $\Omega$. Prove the distributive law
$$
(A \cup B) \cap C=(A \cap C) \cup(B \cap C) .
$$

Probability, Statistics, and Queuing Theory with Computer Science Applications, Second Edition (Computer Science and Scientific Computing)

Probability, Statistics, and Queuing Theory with Computer Science Applications, Second Edition (Computer Science and Scientific Computing)

Arnold O. Allen 2nd Edition

Chapter 2, Problem 3

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Step 1

Let $A$, $B$, and $C$ be subsets of a sample space $\Omega$. We need to prove that: $$(A \cup B) \cap C = (A \cap C) \cup (B \cap C).$$ Show more…

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Suppose $A, B$, and $C$ are events in some sample space $\Omega$, and thus are subsets of $\Omega$. Prove the distributive law $$ (A \cup B) \cap C=(A \cap C) \cup(B \cap C) . $$

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