Consider the following statements for the two non-empty sets A and B.

1. $$(A \cap B) \cup (A \cap \overline B ) \cup (\overline A \cap B) = A \cup B$$

2. $$(A \cup (\overline A \cap \overline B )) = A \cup B$$

Which of the above statements is/are correct?

Let X be a non-empty set and let A, B, C be subsets of X. Consider the following statements.

1. $$A \subset C \Rightarrow (A \cap B) \subset (C \cap B),\,(A \cup B) \subset (C \cup B)$$

2. $$(A \cap B) \subset (C \cap B)$$ for all sets $$B \Rightarrow A \subset C$$

3. $$(A \cup B) \subset (C \cup B)$$ for all sets $$B \Rightarrow A \subset C$$

Which of the above statements are correct?

If A = {$$\lambda$$, {$$\lambda$$, $$\mu$$}}, then the power set of A is

In a school, all the students play atleast one of thee indoor games - chess, carrom and table tennis. 60 play chess, 50 play table tennis, 48 play carrom, 12 play chess and carrom, 15 play carrom and table tennis, 20 play table tennis and chess.

What can be the minimum number of students in the school?