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மூன்று கணங்களின் சேர்ப்புக்கான சேர்ப்பு பண்பு:
\(A\),\(B\) மற்றும் \(C\) என்பன மூன்று கணம் எனில், \(A \cup (B \cup C)\) \(=\) \((A \cup B) \cup C\)
எடுத்துக்காட்டாக,
\(A \cup (B \cup C)\)
\(B \cup C\) \(=\) \(\{11\), \(12\), \(13\)\(\}\) \(\cup\) \(\{\)\(12\), \(13\), \(14\)\(\}\)
\(B \cup C\) \(=\) \(\{\)\(11\), \(12\), \(13\), \(14\)\(\}\)
\(A \cup (B \cup C)\) \(=\) \(\{\)\(10\), \(11\), \(12\)\(\}\) \(\cup\) \(\{\)\(11\), \(12\), \(13\), \(14\)\(\}\)
\(A \cup (B \cup C)\) \(=\) \(\{\)\(10\), \(11\), \(12\), \(13\), \(14\)\(\}\) - - - - - - \((I)\)
\((A \cup B) \cup C\)
\(A \cup B\) \(=\) \(\{\)\(10\), \(11\), \(12\)\(\}\) \(\cup\) \(\{11\), \(12\), \(13\)\(\}\)
\(A \cup B\) \(=\) \(\{\)\(10\), \(11\), \(12\), \(13\)\(\}\)
\((A \cup B) \cup C\) \(=\) \(\{\)\(10\), \(11\), \(12\), \(13\)\(\}\) \(\cup\) \(\{\)\(12\), \(13\), \(14\)\(\}\)
\((A \cup B) \cup C\) \(=\) \(\{\)\(10\), \(11\), \(12\), \(13\), \(14\)\(\}\) - - - - - - \(\(II)\)
\((I)\) மற்றும் \((II)\) இருந்து,
\(A \cup (B \cup C)\) \(=\) \((A \cup B) \cup C\)
மூன்று கணங்களின் வெட்டுக்கான சேர்ப்பு பண்பு:
\(A\),\(B\)மற்றும்\(C\) என்பன மூன்று கணம் எனில், \(A \cap (B \cap C)\) \(=\) \((A \cap B) \cap C\)
எடுத்துக்காட்டாக,
\(A\) \(=\) \(\{\)\(a\), \(b\), \(c\), \(d\)\(\}\), \(B\) \(=\) \(\{c\), \(d\), \(e\)\(\}\) மற்றும் \(C\) \(=\) \(\{\)\(d\), \(e\), \(f\)\(\}\)
\(A \cap (B \cap C)\)
\(B \cap C\) \(=\) \(\{c\), \(d\), \(e\)\(\}\) \(\cap\) \(\{\)\(d\), \(e\), \(f\)\(\}\)
\(B \cap C\) \(=\) \(\{\)\(d\), \(e\)\(\}\)
\(A \cap (B \cap C)\) \(=\) \(\{\)\(a\), \(b\), \(c\), \(d\)\(\}\) \(\cap\) \(\{\)\(d\), \(e\)\(\}\)
\(A \cap (B \cap C)\) \(=\) \(\{\)\(d\)\(\}\) - - - - - - \((I)\)
\((A \cap B) \cap C\)
\(A \cap B\) \(=\) \(\{\)\(a\), \(b\), \(c\), \(d\)\(\}\) \(\cap\) \(\{c\), \(d\), \(e\)\(\}\)
\(A \cap B\) \(=\) \(\{c\), \(d\)\(\}\)
\((A \cap B) \cap C\) \(=\) \(\{c\), \(d\)\(\}\) \(\cap\) \(\{\)\(d\), \(e\), \(f\)\(\}\)
\((A \cap B) \cap C\) \(=\) \(\{\)\(d\)\(\}\) - - - - - - \((II)\)
\((I)\) மற்றும் \((II)\) இல் இருந்து:
\(A \cap (B \cap C)\) \(=\) \((A \cap B) \cap C\)
இதுவே கணங்களின் சேர்ப்பு பண்பு ஆகும்.
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