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Sets — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSets4 Marks
Question
Let $A = {1, 2, 4, 5}, B = {2, 3, 5, 6}, C = {4, 5, 6, 7}$. Verify the following identities: $\text{A}-(\text{B}\cap\text{C})=(\text{A}-\text{B})\cup(\text{A}-\text{C})$
✓

Answer

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

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