جواب تمرین صفحه 14 درس 1 ریاضی نهم (مجموعه ها)

الف

\(\begin{array}{l}A \cup B = \left\{ {1\,,\,2\,,\,3\,,\,4\,,\,5\,,\,6\,,\,7\,,\,8\,,\,9} \right\}\\\\ \Rightarrow n(A \cup B) = 9\end{array}\)

ب

\(\begin{array}{l}B \cup C = \left\{ {1\,,\,3\,,\,5\,,\,7\,,\,9\,,\,10\,,\,11} \right\}\\\\ \Rightarrow n(B \cup C) = 7\end{array}\)

ج

\(\begin{array}{l}A \cup C = \left\{ {1\,,\,2\,,\,4\,,\,6\,,\,7\,,\,8\,,\,9\,,\,10\,,\,11} \right\}\\\\ \Rightarrow n(A \cup C) = 9\end{array}\)

د

\(\begin{array}{l}A \cap B = \left\{ 9 \right\}\\\\ \Rightarrow n(A \cap B) = 1\end{array}\)

هـ

\(\begin{array}{l}A - B = \left\{ {2\,,\,4\,,\,6\,,\,8} \right\}\\\\ \Rightarrow n(A - B) = 4\end{array}\)

و

\(\begin{array}{l}C - B = \left\{ {10\,,\,11} \right\}\\\\ \Rightarrow n(C - B) = 2\end{array}\)

ز

\(\begin{array}{l}(A - C) \cup (B - C) = \\\\\left\{ {2\,,\,4\,,\,6\,,\,8\,,\,9} \right\} \cup \left\{ {3\,,\,5\,,\,9} \right\} = \\\\\left\{ {2\,,\,3\,,\,4\,,\,5\,,\,6\,,\,8\,,\,9} \right\}\\\\ \Rightarrow n((A - C) \cup (B - C)) = 7\end{array}\)

ح

\(\begin{array}{l}(A \cup B) - C = \\\\\left\{ {1\,,\,2\,,\,3\,,\,4\,,\,5\,,\,6\,,\,7\,,\,8\,,\,9} \right\} - \left\{ {1\,,\,7\,,\,10\,,\,11} \right\} = \\\\\left\{ {2\,,\,3\,,\,4\,,\,5\,,\,6\,,\,8\,,\,9} \right\}\\\\ \Rightarrow n((A \cup B) - C) = 7\end{array}\)

ط

\(\begin{array}{l}A \cap A = \\\\\left\{ {2\,,\,4\,,\,6\,,\,8\,,\,9} \right\} \cap \left\{ {2\,,\,4\,,\,6\,,\,8\,,\,9} \right\} = \\\\\left\{ {2\,,\,4\,,\,6\,,\,8\,,\,9} \right\} = A\\\\ \Rightarrow n(A \cap A) = 5\end{array}\)

ی

\(\begin{array}{l}A \cap \emptyset = \\\\\left\{ {2\,,\,4\,,\,6\,,\,8\,,\,9} \right\} \cap \left\{ {} \right\} = \\\\\left\{ {} \right\} = \emptyset \\\\ \Rightarrow n(A \cap \emptyset ) = 0\end{array}\)

ک

\(\begin{array}{l}B \cup B = \\\\\left\{ {1\,,\,5\,,\,7\,,\,3\,,\,9} \right\} \cup \left\{ {1\,,\,5\,,\,7\,,\,3\,,\,9} \right\} = \\\\\left\{ {1\,,\,5\,,\,7\,,\,3\,,\,9} \right\} = B\\\\ \Rightarrow n(B \cup B) = 5\end{array}\)

ل

\(\begin{array}{l}C \cup \emptyset = \left\{ {1\,,\,7\,,\,10\,,\,11} \right\} \cup \emptyset = \\\\\left\{ {1\,,\,7\,,\,10\,,\,11} \right\} = C\\\\ \Rightarrow n(C \cup \emptyset ) = 4\end{array}\)

الف

درست

ب

درست

\(\begin{array}{l}(A - B) \cup (A \cap B) = \\\\\left\{ {1\,\,,\,2\,,\,9} \right\} \cup \left\{ {3\,,\,4\,,\,5} \right\} = \\\\\left\{ {1\,\,,\,2\,,\,9\,,\,3\,,\,4\,,\,5} \right\} = A\end{array}\)

ج

نادرست

\(\begin{array}{l}(A - B) \cup (B - A) = \\\\\left\{ {1\,,\,2\,,\,9} \right\} \cup \left\{ {6\,,\,7} \right\} = \left\{ {1\,,\,2\,,\,9\,,\,6\,,\,7} \right\}\end{array}\)

د

درست

هـ

نادرست؛ در صورتی که \(A - B = B - A\) درست می باشد که \(A = B\) باشد.

و

نادرست

\(\begin{array}{l}n(A - B) = 3\\\\n(B - A) = 2\end{array}\)

الف

اشتراک دو مجموعه، زیر مجموعهٔ اجتماع همان دو مجموعه است.

ب

هریک از دو مجموعهٔ A و B زیرمجموعهٔ \(A \cup B\) است.

ج

اشتراک دو مجموعهٔ A و B زیرمجموعۀ هر یک از دو مجموعهٔ A و B است.

د

مجموعهٔ A-B زیرمجموعهٔ مجموعهٔ A است.

هـ

اجتماع دو مجموعهٔ \((B - A)\) و \((A \cap B)\) با مجموعهٔ B مساوی است.