Question # 01: Four option are given against each statement. Encircle the correct option.
\((i)\) The set builder form of the set \(\{1,\frac{1}{3} ,\frac{1}{5} ,\frac{1}{7} ,\dotsc \}\) is:
\( a) \quad \) \( \{x\mid x=\frac{1}{n} ,n\in W\} \)
\( b) \quad \) \( \{x\mid x=\frac{1}{2n+1} ,n\in W\}\)
\(c) \quad \) \( \{x\mid x=\frac{1}{n+1} ,n\in W\}\)
\( d) \quad \) \( \{x\mid x=2n+1,n\in W\}\)
Answer: \( b) \; \) \( \{x\mid x=\frac{1}{2n+1} ,n\in W\}\)
Explanation:
Try substituting values of \(n=0,1,2,3,…\) into each option. In option (b), doing this gives the set: \(\{1,\frac{1}{3} ,\frac{1}{5} ,\frac{1}{7} ,\dotsc \}\)