Prove That A ∩ B ⊂ A
Question:
For any two sets \( A \) and \( B \), prove that:
\[ A\cap B \subset A \]Solution
Let \( x\in A\cap B \).
By the definition of intersection of sets, \( x \) belongs to both \( A \) and \( B \).
Therefore,
\[ x\in A \]Hence every element of \( A\cap B \) is also an element of \( A \).
Therefore,
\[ A\cap B \subset A \]Hence proved.