For any two sets A and B, prove that. A =A. - Vidyadip

Question

For any two sets A and B, prove that. $\text{A}\subset\text{B}\Rightarrow\text{A}\cap\text{B}=\text{A}.$

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Answer

Let $\text{x}\in\text{A}\subset\text{B}.$ Then $\Rightarrow\text{x}\in\text{B}$ Let and $\text{x}\in\text{A}\cap\text{B}$ $\Leftrightarrow\text{x}\in\text{A and x}\in\text{B}$ $\Leftrightarrow\text{x}\in\text{A and x}\in\text{A}$ $(\because\text{A}\subset\text{B})$ $\therefore(\text{A}\cap\text{B})=\text{A}.$

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