Question

N(A ∩ B) = 3 , n(A) = 7, n(B) = 9 → n ( A U B ) = ?

Answer 1

Ответ:

13

Пошаговое объяснение:

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Answer 2

The formula you're using relates to the cardinality of sets. In this context:

• $N(X)$ represents the number of elements in set $X$.
• $A \cap B$ represents the intersection of sets $A$ and $B$, which is the set of elements that are common to both $A$ and $B$.
• $A \cup B$ represents the union of sets $A$ and $B$, which is the set of all elements that belong to either $A$ or $B$ or both.

Given the information you've provided:

• $N(A \cap B) = 3$ implies that there are 3 elements that are common to both sets $A$ and $B$.
• $N(A) = 7$ implies that there are 7 elements in set $A$.
• $N(B) = 9$ implies that there are 9 elements in set $B$.

To find $N(A \cup B)$, which is the number of elements in the union of sets $A$ and $B$, you can use the inclusion-exclusion principle:

$N(A \cup B) = N(A) + N(B) - N(A \cap B).$

Substituting the given values:

$N(A \cup B) = 7 + 9 - 3 = 13.$

Therefore, $N(A \cup B) = 13$, which means there are 13 elements in the union of sets $A$ and $B$.