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Free CBSE - Class 11 Mathematics - Sets worksheets

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1.
Show that for any sets $A$ and $B$, $A = ( A \cap B ) \cup ( A – B )$ and $A \cup ( B – A ) = ( A \cup B )$
2.
Using properties of sets, show that (i) $A \cup ( A \cap B ) = A$
3.
Using properties of sets, show that (ii) $A \cap ( A \cup B ) = A$.
4.
Show that $A \cap B = A \cap C$ need not imply $B = C$.
5.
Let $A$ and $B$ be sets. If $A \cap X = B \cap X = \phi$ and $A \cup X = B \cup X$ for some set $X$, show that $A = B$. (Hints $A = A \cap ( A \cup X ) , B = B \cap ( B \cup X )$ and use Distributive law )
6.
Find sets $A, B$ and $C$ such that $A \cap B, B \cap C$ and $A \cap C$ are non-empty sets and $A \cap B \cap C = \phi$.
7.
In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example. (iv) If $A \not\subset B$ and $B \not\subset C$, then $A \not\subset C$
8.
Let $A, B$, and $C$ be the sets such that $A \cup B = A \cup C$ and $A \cap B = A \cap C$. Show that $B = C$.
9.
Show that the following four conditions are equivalent : (i) $A \subset B$
10.
Show that the following four conditions are equivalent : (ii) $A – B = \phi$
- OR -

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