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சேர்ப்பின் மீதான வெட்டின் பங்கீட்டுப் பண்பு:
\(A\), \(B\) மற்றும் \(C\)என்பன ஏதேனும் மூன்று கணங்கள் எனில் , \(A \cap (B \cup C)\) \(=\) \((A \cap B)\) \(\cup\) \((A \cap C)\)
எடுத்துக்காட்டாக,
\(A\) \(=\) \(\{\)\(l\), \(m\), \(n\), \(o\), \(p\)\(\}\), \(B\) \(=\) \(\{\)\(n\), \(o\), \(p\), \(q\), \(r\)\(\}\text{மற்றும்}\) \(C\) \(=\) \(\{\)\(l\), \(n\), \(p\), \(r\)\(\}\)
\(A \cap (B \cup C)\)
\(B \cup C\) \(=\) \(\{\)\(n\), \(o\), \(p\), \(q\), \(r\)\(\}\) \(\cup\) \(\{\)\(l\), \(n\), \(p\), \(r\)\(\}\)
\(B \cup C\) \(=\) \(\{\)\(l\), \(n\), \(o\), \(p\), \(q\), \(r\)\(\}\)
\(A \cap (B \cup C)\) \(=\) \(\{\)\(l\), \(m\), \(n\), \(o\), \(p\)\(\}\) \(\cap\) \(\{\)\(l\), \(n\), \(o\), \(p\), \(q\), \(r\)\(\}\)
\(A \cap (B \cup C)\) \(=\) \(\{\)\(l\), \(n\), \(o\), \(p\)\(\}\) - - - - - - - - - (I)
\((A \cap B)\) \(\cup\) \((A \cap C)\)
\(A \cap B\) \(=\) \(\{\)\(l\), \(m\), \(n\), \(o\), \(p\)\(\}\) \(\cap\) \(\{\)\(n\), \(o\), \(p\), \(q\), \(r\)\(\}\)
\(A \cap B\) \(=\) \(\{\)\(n\), \(o\), \(p\)\(\}\)
\(A \cap C\) \(=\) \(\{\)\(l\), \(m\), \(n\), \(o\), \(p\)\(\}\) \(\cap\) \(\{\)\(l\), \(n\), \(p\), \(r\)\(\}\)
\(A \cap C\) \(=\) \(\{\)\(l\), \(n\), \(p\)\(\}\)
\((A \cap B)\) \(\cup\) \((A \cap C)\) \(=\) \(\{\)\(n\), \(o\), \(p\)\(\}\) \(\cup\) \(\{\)\(l\), \(n\), \(p\)\(\}\)
\((A \cap B)\) \(\cup\) \((A \cap C)\) \(=\) \(\{\)\(l\), \(n\), \(o\), \(p\)\(\}\) - - - - - - - - - (II)
(I) மற்றும் (II) இல் இருந்து,
\(A \cap (B \cup C)\) \(=\) \((A \cap B)\) \(\cup\) \((A \cap C)\)
வெட்டின் மீதான சேர்ப்பின் பங்கீட்டுப் பண்பு:
\(A\), \(B\) மற்றும் \(C\) என்பன ஏதேனும் மூன்று கணங்கள் எனில், \(A \cup (B \cap C)\) \(=\) \((A \cup B)\) \(\cap\) \((A\cup C)\)
எடுத்துக்காட்டாக,
\(A\) \(=\) \(\{\)\(l\), \(m\), \(n\), \(o\), \(p\)\(\}\), \(B\) \(=\) \(\{\)\(n\), \(o\), \(p\), \(q\), \(r\)\(\}\) மற்றும் \(C\) \(=\) \(\{\)\(l\), \(n\), \(p\), \(r\)\(\}\)
\(A \cup (B \cap C)\)
\(B \cap C\) \(=\) \(\{\)\(n\), \(o\), \(p\), \(q\), \(r\)\(\}\) \(\cap \) \(\{\)\(l\), \(n\), \(p\), \(r\)\(\}\)
\(B \cap C\) \(=\) \(\{\)\(n\), \(p\), \(r\)\(\}\)
\(A \cup (B \cap C)\) \(=\) \(\{\)\(l\), \(m\), \(n\), \(o\), \(p\)\(\}\) \(\cup \) \(\{\)\(n\), \(p\), \(r\)\(\}\)
\(A \cup (B \cap C)\) \(=\) \(\{\)\(l\), \(m\), \(n\), \(o\), \(p\), \(r\)\(\}\) - - - - - - - - - (I)
\((A \cup B)\) \(\cap\) \((A \cup C)\)
\(A \cup B\) \(=\) \(\{\)\(l\), \(m\), \(n\), \(o\), \(p\)\(\}\) \(\cup \) \(\{\)\(n\), \(o\), \(p\), \(q\), \(r\)\(\}\)
\(A \cup B\) \(=\) \(\{\)\(l\), \(m\), \(n\), \(o\), \(p\), \(q\), \(r\)\(\}\)
\(A \cup C\) \(=\) \(\{\)\(l\), \(m\), \(n\), \(o\), \(p\)\(\}\) \(\cup \) \(\{\)\(l\), \(n\), \(p\), \(r\)\(\}\)
\(A \cup C\) \(=\) \(\{\)\(l\), \(m\), \(n\), \(o\), \(p\), \(r\)\(\}\)
\((A \cup B)\) \(\cap \) \((A \cup C)\) \(=\) \(\{\)\(l\), \(m\), \(n\), \(o\), \(p\), \(q\), \(r\)\(\}\) \(\cap \) \(\{\)\(l\), \(m\), \(n\), \(o\), \(p\), \(r\)\(\}\)
\((A \cup B)\) \(\cap \) \((A \cup C)\) \(=\) \(\{\)\(l\), \(m\), \(n\), \(o\), \(p\), \(r\)\(\}\) - - - - - - - - - (II)
(I) மற்றும் (II) இல் இருந்து,
\(A \cup (B \cap C)\) \(=\) \((A \cup B)\) \(\cap \) \((A \cup C)\)
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