Exercise 1.1-Additional Problems - Chapter 1 - Sets, Relations and Functions - 11th Maths Guide Samacheer Kalvi Solutions

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Additional Questions
Question 1.
Write the following sets in roster form
(a) $\left\{\mathrm{x} \in \mathrm{N} ; \mathrm{x}^3<1000\right\}$
(b) $\left\{\right.$ The set of positive roots of the equation $\left.\left(x^2-4\right)\left(x^3-27\right)=0\right\}$
Solution:
(a) $\mathrm{A}=\{1,2,3,4,5,6,7,8,9\}$
(b) $\mathrm{B}=\{2,3\}$
Question 2.
By taking suitable sets $A, B, C$ verify the following results
(i) $\mathrm{A} \times(\mathrm{B} \cup \mathrm{C})=(\mathrm{A} \times \mathrm{B}) \cup(\mathrm{A} \times \mathrm{C})$
(ii) $(B-A) \cup C=(B \cup C)-(A-C)$
Solution:
Prove by yourself

Question 3.
Given $n(A)=7 ; n(B)=8$ and $n(A \cup B)=10$ find $n[P(A \cap B)]$.
Solution:
$
\begin{aligned}
& \mathrm{n}(\mathrm{A} \cup \mathrm{B})=\mathrm{n}(\mathrm{A})+\mathrm{n}(\mathrm{B})-\mathrm{n}(\mathrm{A} \cap \mathrm{B}) \\
& \text { (i.e., } 10=7+8-\mathrm{n}(\mathrm{A} \cap \mathrm{B}) \\
& \Rightarrow \mathrm{n}(\mathrm{A} \cap \mathrm{B})=7+8-10=5 \\
& \text { So } \mathrm{n}[\mathrm{P}(\mathrm{A} \cap \mathrm{B})]=25=32
\end{aligned}
$