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Question

# Prove the second absorption law by showing that if A and B are sets, then A ∩ (A ∪ B) = A.

Solution

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DEFINITIONS

$\textbf{Union}$ $A\cup B$: All elements that are either in $A$ OR in $B$

$\textbf{Intersection}$ $A\cap B$: All elements that are both in $A$ AND in $B$.

$\textbf{Disjunction}$ $p\vee q$: $p$ or $q$

$\textbf{Conjunction}$ $p\wedge q$: $p$ and $q$

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