Davies Valdez
05/14/2024 · Junior High School

If \( A \cap B=B \), then

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If \( A \cap B = B \), this means that every element of set \( B \) is also an element of set \( A \). In set theory, this can be interpreted as saying that set \( B \) is a subset of set \( A \). In formal notation, we can express this as: \[ B \subseteq A \] This relationship holds because the intersection of \( A \) and \( B \) contains all elements that are common to both sets, and since the intersection equals \( B \), it indicates that all elements of \( B \) are indeed found in \( A \). Thus, the conclusion is: \[ B \subseteq A \]

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\( B \subseteq A \)
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