PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions

For any two sets, prove that: 

\[A \cup \left( A \cap B \right) = A\] 

For any two sets, prove that: 

\[A \cap \left( A \cup B \right) = A\]

Find sets A, B and C such that \[A \cap B, A \cap C \text{ and } B \cap C\]are non-empty sets and\[A \cap B \cap C = \phi\]

For any two sets A and B, prove that: \[A \cap B = \phi \Rightarrow A \subseteq B'\] 

If A and B are sets, then prove that  \[A - B, A \cap B \text{ and } B - A\] are pair wise disjoint. 

Using properties of sets, show that for any two sets A and B,\[\left( A \cup B \right) \cap \left( A \cap B' \right) = A\] 

For any two sets of A and B, prove that: 

\[A' \cup B = U \Rightarrow A \subset B\] 

For any two sets of A and B, prove that: 

\[B' \subset A' \Rightarrow A \subset B\]

Is it true that for any sets A and \[B, P \left( A \right) \cup P \left( B \right) = P \left( A \cup B \right)\]? Justify your answer.

Show that for any sets A and B, A = (A ∩ B) ∪ ( A - B)

Show that for any sets A and B, A ∪ (B – A) = (A ∪ B)

Each set X, contains 5 elements and each set Y, contains 2 elements and \[\cup^{20}_{r = 1} X_r = S = \cup^n_{r = 1} Y_r\] If each element of S belong to exactly 10 of the X_r's and to eactly 4 of Y_r's, then find the value of n.

For any two sets A and B, prove that : 

\[A' - B' = B - A\] 

For any two sets A and B, prove the following: 

\[A \cap \left( A' \cup B \right) = A \cap B\] 

For any two sets A and B, prove the following: 

\[A - \left( A - B \right) = A \cap B\]

For any two sets A and B, prove the following: 

\[A \cap \left( A \cup B \right)' = \phi\] 

For any two sets A and B, prove the following:

\[A - B = A \Delta\left( A \cap B \right)\]

Let A and B be two sets such that : \[n \left( A \right) = 20, n \left( A \cup B \right) = 42 \text{ and } n \left( A \cap B \right) = 4\] \[n \left( A - B \right)\]

Let A and B be two sets such that : \[n \left( A \right) = 20, n \left( A \cup B \right) = 42 \text{ and } n \left( A \cap B \right) = 4\] \[n \left( B - A \right)\]

A survey shows that 76% of the Indians like oranges, whereas 62% like bananas. What percentage of the Indians like both oranges and bananas?