Question

Set builder from of A={1,1/4,1/9,1/16,1/25

Answer 1

$\green{\large\underline{\sf{Given- }}}$

$\rm :\longmapsto\:A = \bigg \{1, \: \dfrac{1}{4}, \: \dfrac{1}{9}, \: \dfrac{1}{16}, \: \dfrac{1}{25} \bigg \}$

$\red{\large\underline{\sf{To\:Find - }}}$

The Set Builder form of set A.

$\blue{\large\underline{\sf{Solution-}}}$

Given Set is

$\rm :\longmapsto\:A = \bigg \{1, \: \dfrac{1}{4}, \: \dfrac{1}{9}, \: \dfrac{1}{16}, \: \dfrac{1}{25} \bigg \}$

To represent this roster form of set in Set Builder form, we have to first find a pattern.

So, above can be rewritten as

$\rm :\longmapsto\:A = \bigg \{ \dfrac{1}{1} , \: \dfrac{1}{2 \times 2}, \: \dfrac{1}{3 \times 3}, \: \dfrac{1}{4 \times 4}, \: \dfrac{1}{5 \times 5} \bigg \}$

$\rm :\longmapsto\:A = \bigg \{ \dfrac{1}{ {1}^{2} } , \: \dfrac{1}{ {2}^{2} }, \: \dfrac{1}{ {3}^{2}} , \: \dfrac{1}{ {4}^{2} }, \: \dfrac{1}{ {5}^{2} } \bigg \}$

So, required Set Builder Form is

$\red{\rm :\longmapsto\:A = \bigg\{x : x = \dfrac{1}{ {n}^{2} }, \: n \: \in \: N \: and \: n \leqslant 5 \: \bigg\}}$

More to know :-

1. Commutative Law :-

$\boxed{ \tt{ \: A\cup B = B\cup A \: }}$

$\boxed{ \tt{ \: A\cap B = B\cap A \: }}$

2. Associative Law

$\boxed{ \tt{ \: (A\cup B)\cup C = A\cup (B\cup C) \: }}$

$\boxed{ \tt{ \: (A\cap B)\cap C = A\cap (B\cap C) \: }}$

3. Distributive Law

$\boxed{ \tt{ \: A\cup (B\cap C \: ) = (A\cup B) \: \cap \: (A\cup C) \: }}$

$\boxed{ \tt{ \: A\cap (B\cup C \: ) = (A\cap B) \: \cup \: (A\cap C) \: }}$

4. De Morgan's Law

$\boxed{ \tt{ \: (A\cup B)' = A' \: \cap \: B' \: }}$

$\boxed{ \tt{ \: (A\cap B)' = A' \: \cup \: B' \: }}$