It is given that the universal set, \(\xi=\{x:x\text{ is an integer, }1\leq x\leq 10\}\), set \(P=\{x:x\text{ is an odd number}\}\), set \(Q=\{x:x\text{ is a prime number}\}\) and
set \(R=\{x:x\text{ is a multiple of 3}\}\).
List all the elements of the \(P\,\cap\,Q\), \(P\,\cap\,R\), \(Q\,\cap\,R\) and \(P\,\cap\,Q\, \cap R\).
|
Answer |
\(P\,\cap\,Q\) |
\(P=\{1,3,5,7,9\}\)
\(Q=\{2,3,5,7\}\)
\(P\,\cap\,Q=\{3,5,7\}\) |
\(P\,\cap\,R\) |
\(P=\{1,3,5,7,9\}\)
\(R=\{3,6,9\}\)
\(P\,\cap\,R=\{3,9\}\) |
\(Q\,\cap\,R\) |
\(Q=\{2,3,5,7\}\)
\(R=\{3,6,9\}\)
\(Q\,\cap\,R=\{3\}\) |
\(P\,\cap\,Q\, \cap R\) |
\(P=\{1,3,5,7,9\}\)
\(Q=\{2,3,5,7\}\)
\(R=\{3,6,9\}\)
\(P\,\cap\,Q\, \cap R=\{3\}\) |
State the number of elements of the \(n(P\,\cap\,Q)\), \(n(P\,\cap\,R)\), \(n(Q\,\cap\,R)\) and \(n(P\,\cap\,Q\, \cap R)\).
|
Answer |
\(n(P\,\cap\,Q)\) |
\(P\,\cap\,Q=\{3,5,7\}\)
\(n(P\,\cap\,Q)=3\) |
\(n(P\,\cap\,R)\) |
\(P\,\cap\,R=\{3,9\}\)
\(n(P\,\cap\,R)=2\) |
\(n(Q\,\cap\,R)\) |
\(Q\,\cap\,R=\{3\}\)
\(n(Q\,\cap\,R)=1\) |
\(n(P\,\cap\,Q\, \cap R)\) |
\(P\,\cap\,Q\, \cap R=\{3\}\)
\(n(P\,\cap\,Q\, \cap R)=1\) |
|