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Sets — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSets3 Marks
Question
Let A = {1, 2, 4, 5}, B = {2, 3, 5, 6}, C = {4, 5, 6, 7}. Verify the following identities: $\text{A}\cap(\text{B}-\text{C})=(\text{A}\cap\text{B})-(\text{A}\cap\text{C})$
✓

Answer

$\text{A} = \{1, 2, 4, 5\},$ $\text{B} = \{2, 3, 5, 6\},$ and $\text{C} = \{4, 5, 6, 7\}$ $\text{B}-\text{C} = \{2, 3\}$ $\text{A}\cap(\text{B}-\text{C}) = \{2\}\ .....(1)$ $(\text{A}\cap\text{B})= \{2, 5\}$ $(\text{A}\cap\text{C})= \{4, 5\}= \{2\}\ .....2)$ $(\text{A}\cap\text{B})-(\text{A}\cap\text{C})$ From $eq^n$ (1) and $eq^n$ (2), we get $\text{A}\cap(\text{B}-\text{C})=(\text{A}\cap\text{B})-(\text{A}\cap\text{C}).$

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