CBSE BoardEnglish MediumSTD 11 ScienceMathsSets2 Marks
Question
For all sets A, B and C, if $\text{A}\subset\text{B},$ then $\text{A}\cup\text{C}\subset\text{B}\cup\text{C}$
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Answer
Suppose $\text{A}\subset\text{B}$ Let $\text{x}\in\text{A}\cup\text{C}$ $\Rightarrow \text{x}\in \text{A}$ or $\text{x}\in\text{C}$ $\Rightarrow \text{x}\in\text{B}$ and $\text{x}\in\text{C}\ \big[\because \text{A}\subset\text{B}\big]$ $\Rightarrow \text{x}\in(\text{B}\cup\text{C})$ $\Rightarrow (\text{A}\cup\text{C})\subset(\text{B}\cup\text{C})$ Hence, the given statement is 'True'.
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