Question
For any two sets A and B , in a universal set U , prove that
A ⊆ B ⇔ A ∪ B = B .
Answer :
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Skip in 10
To prove this, we need to show that: \( A \subseteq B \iff A \cup B = B \) This is a proof of the equivalence of two statements: ### (1) \( A \subseteq B \Rightarrow A \cup B = B \) Let us assume that \( A \subseteq B \). By the definition of subset, this means that every element of \( A \) is also an element of \( B \). Now, consider the union of sets \( A \cup B \). The union consists of all elements that are in either \( A \) or \( B
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