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If X and Y are two sets then X∩(Y∪X)′ equals:

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$\begin{array}{l} \text { We have } \mathrm{X} \cap(\mathrm{Y} \cup \mathrm{X})^{\prime}=\mathrm{X} \cap\left(\mathrm{Y}^{\prime} \cap \mathrm{X}^{\prime}\right) \\ =\mathrm{X} \cap \mathrm{Y}^{\prime} \cap \mathrm{X}^{\prime}=\mathrm{X} \cap \mathrm{X}^{\prime} \cap \mathrm{Y}^{\prime} \\ =\phi \cap \mathrm{Y}^{\prime}=\phi \end{array}$

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