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