Tamil Nadu Board Solutions for Chapter: Sets, Relations and Functions, Exercise 1: Exercise

By taking suitable sets $A, B, C$ verify the following result:

$(B-A)\cap C=(B\cap C)-A=B\cap (C-A)$

By taking suitable sets $A, B, C$ verify the following result:

$(B-A)\cup C=(B\cup C)-(A-C)$

Justify the trueness of the statement:

“An element of a set can never be a subset of itself.”

If $n\left(P\right(A\left)\right)=1024, n(A\cup B)=15$ and $n\left(P\right(B\left)\right)=32$ then find $n(A\cap B)$ 

If $n(A\cap B)=3$ and $n(A\cup B)=10$ then find $n\left(P\right(A\Delta B\left)\right)$.

For a set $A$, $A\times A$ contains$16$ elements and two of its elements are $\left(1,3\right)$ and $\left(0,2\right)$ Find the elements of $A$.

Let $A$ and $B$ be two sets such that $n\left(A\right)=3$ and $n\left(B\right)=2$.If $(x, 1),(y, 2),(z, 1)$ are in $A\times B$, find $A$ and $B$, where $x, y, z$ are distinct elements.

If $A\times A$ has $16$ elements, $S=\left\{\right(a,b)\in A\times A:a<b\}$; $(-1,2)$ and $\left(0,1\right)$ are two elements of $S$, then find the remaining elements of $S$.