Question
Let $A=\{a, e, i, o, u\}, B=\{a, d, e, o, v)$ and $C=\{e, o, t, m]$. Using Venn diagrams, verify that: $A \cup(B \cap C)=$ $(A \cup B) \cap(A \cup C)$
✓
Answer
Here, it is given: $A =\{ a , e , i , o , u \}, B =\{ a , d , e , o , v \}$ and $C =\{ e , o , t , m \}$.
$B \cap C=\{e, o\}$ and $A \cup(B \cap C)=\{a, e, i, o, u\}$
$\text{LHS}$
$\text{R.H.S:} A \cup B=\{a, d, e, I, o, u, v\}$ and $A \cup C=\{a, e, I, o, u, t, m\}$
$(A \cup B) \cap(A \cup C)=\{a, e, I, o, u\}$
$\text { L.H.S = R.H.S. }[$ Verified$]$
$B \cap C=\{e, o\}$ and $A \cup(B \cap C)=\{a, e, i, o, u\}$
$\text{LHS}$
$\text{R.H.S:} A \cup B=\{a, d, e, I, o, u, v\}$ and $A \cup C=\{a, e, I, o, u, t, m\}$
$(A \cup B) \cap(A \cup C)=\{a, e, I, o, u\}$
$\text { L.H.S = R.H.S. }[$ Verified$]$
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