Show that $A \cap B=A \cap C$ need not imply $B = C$
Show that $A \cap B=A \cap C$ need not imply $B = C$
Let $A=\{0,1\}, B=\{0,2,3\},$ and $C=\{0,4,5\}$
Accordingly, $A \cap B=\{0\}$ and $A \cap C=\{0\}$
Here, $A \cap B=A \cap C=\{0\}$
However, $B \ne C\,[2 \in B$ and $2 \notin C]$
Similar Questions
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$A \cap \left( {B \cup D} \right)$
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If $S$ and $T$ are two sets such that $S$ has $21$ elements, $T$ has $32$ elements, and $S$ $\cap \,T$ has $11$ elements, how many elements does $S\, \cup$ $T$ have?
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State whether each of the following statement is true or false. Justify you answer.
$\{2,6,10\}$ and $\{3,7,11\}$ are disjoint sets.
State whether each of the following statement is true or false. Justify you answer.
$\{2,6,10\}$ and $\{3,7,11\}$ are disjoint sets.
Using that for any sets $\mathrm{A}$ and $\mathrm{B},$
$A \cup(A \cap B)=A$
Using that for any sets $\mathrm{A}$ and $\mathrm{B},$
$A \cup(A \cap B)=A$