For Any Two Sets of a and B, Prove That: a ′ ∪ B = U ⇒ a ⊂ B - Mathematics

Question

For any two sets of A and B, prove that:

\[A' \cup B = U \Rightarrow A \subset B\]

Solution

\[\ \text{ Let } a \in A . \]
\[ \Rightarrow a \in U\]
\[ \Rightarrow a \in A' \cup B \left( \because U = A' \cup B \right)\]
\[ \Rightarrow a \in B \left( \because a \not\in A' \right)\]
\[\text{ Hence }, A \subset B . \]

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Types of Sets - Universal Set

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Q 12.1 Q 11 Q 12.2

Chapter 1: Sets - Exercise 1.06 [Page 27]

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RD Sharma Mathematics [English] Class 11

Chapter 1 Sets
Exercise 1.06 | Q 12.1 | Page 27

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