Question

Write the set $H=\{5,5^2,5^3,5^4\}$ in the set builder form.

• A. $H=\{x|x=5^{n-1},n\in N,n\le 4\}$
• B. $H=\{x|x=5^n,n\in N,n\le 4\}$
• C. $H=\{x|x=5^{n-1},n\in N,n<4\}$
• D. Data insufficient
  

Answer 1

Answer: (B)

$H=\{x|x=5^n,n\in N,n\le 4\}$

In set builder form of representation of a set, the element of the set is described by using a symbol x or any other variable followed by a colon, the symbol : or | is used to denote such that and then we write the property possessed by the elements of the set and enclose the whole description in braces. In this, the colon stands for such that and braces stand for set of all.

Hence, $H=\{x|x=5^n,n\in N,n\le 4\}$