PUMPA - SMART LEARNING
எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்
Book Free DemoAssociative property for union of three sets
You can group three sets in any order, and the union of three sets will be the same.
\(A \cup (B \cup C)\) \(=\) \((A \cup B) \cup C\)
Let \(A\) \(=\) \(\{\)\(10\), \(11\), \(12\)\(\}\), \(B\) \(=\) \(\{11\), \(12\), \(13\)\(\}\) and \(C\) \(=\) \(\{\)\(12\), \(13\), \(14\)\(\}\).
L.H.S: \(A \cup (B \cup C)\)
\(B \cup C\) \(=\) \(\{11\), \(12\), \(13\)\(\}\) \(\cup\) \(\{\)\(12\), \(13\), \(14\)\(\}\)
\(B \cup C\) \(=\) \(\{\)\(11\), \(12\), \(13\), \(14\)\(\}\)
\(A \cup (B \cup C)\) \(=\) \(\{\)\(10\), \(11\), \(12\)\(\}\) \(\cup\) \(\{\)\(11\), \(12\), \(13\), \(14\)\(\}\)
\(A \cup (B \cup C)\) \(=\) \(\{\)\(10\), \(11\), \(12\), \(13\), \(14\)\(\}\) - - - - - - (I)
R.H.S: \((A \cup B) \cup C\)
\(A \cup B\) \(=\) \(\{\)\(10\), \(11\), \(12\)\(\}\) \(\cup\) \(\{11\), \(12\), \(13\)\(\}\)
\(A \cup B\) \(=\) \(\{\)\(10\), \(11\), \(12\), \(13\)\(\}\)
\((A \cup B) \cup C\) \(=\) \(\{\)\(10\), \(11\), \(12\), \(13\)\(\}\) \(\cup\) \(\{\)\(12\), \(13\), \(14\)\(\}\)
\((A \cup B) \cup C\) \(=\) \(\{\)\(10\), \(11\), \(12\), \(13\), \(14\)\(\}\) - - - - - - (II)
From (I) and (II), we see that:
\(A \cup (B \cup C)\) \(=\) \((A \cup B) \cup C\)
This is called associative property of union of three sets.
Associative property for intersection of three sets
You can group three sets in any order, and the intersection of three sets will be the same.
\(A \cap (B \cap C)\) \(=\) \((A \cap B) \cap C\)
Let \(A\) \(=\) \(\{\)\(a\), \(b\), \(c\), \(d\)\(\}\), \(B\) \(=\) \(\{c\), \(d\), \(e\)\(\}\) and \(C\) \(=\) \(\{\)\(d\), \(e\), \(f\)\(\}\)
L.H.S: \(A \cap (B \cap C)\)
\(B \cap C\) \(=\) \(\{c\), \(d\), \(e\)\(\}\) \(\cap\) \(\{\)\(d\), \(e\), \(f\)\(\}\)
\(B \cap C\) \(=\) \(\{\)\(d\), \(e\)\(\}\)
\(A \cap (B \cap C)\) \(=\) \(\{\)\(a\), \(b\), \(c\), \(d\)\(\}\) \(\cap\) \(\{\)\(d\), \(e\)\(\}\)
\(A \cap (B \cap C)\) \(=\) \(\{\)\(d\)\(\}\) - - - - - - (I)
R.H.S: \((A \cap B) \cap C\)
\(A \cap B\) \(=\) \(\{\)\(a\), \(b\), \(c\), \(d\)\(\}\) \(\cap\) \(\{c\), \(d\), \(e\)\(\}\)
\(A \cap B\) \(=\) \(\{c\), \(d\)\(\}\)
\((A \cap B) \cap C\) \(=\) \(\{c\), \(d\)\(\}\) \(\cap\) \(\{\)\(d\), \(e\), \(f\)\(\}\)
\((A \cap B) \cap C\) \(=\) \(\{\)\(d\)\(\}\) - - - - - - (II)
From (I) and (II), we see that:
\(A \cap (B \cap C)\) \(=\) \((A \cap B) \cap C\)
This is called associative property of intersection of three sets.
Important!
L.H.S – Left Hand Side
R.H.S – Right Hand Side
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