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JEE Main 201412 AprilOnline
Exam
JEE Main
Year
2014
Date
12 April
Mode
Online
Subject
Mathematics
Chapter
Sets and Relations

JEE Main 2014 · 12 April · Online · Mathematics · Sets and Relations

A relation on the set A=\ x:|x| < 3, x ∈ Z\ , where Z is the set of...

A relation on the set A={x:∣x∣<3,x∈Z}\mathrm{A}=\{\mathrm{x}:|\mathrm{x}| < 3, \mathrm{x} \in \mathrm{Z}\}, where ZZ is the set of integers is defined by R={(x,y):y=∣x∣,x≠−1}\mathrm{R}=\{(\mathrm{x}, \mathrm{y}): \mathrm{y}=|\mathrm{x}|, \mathrm{x} \neq-1\}. Then the number of elements in the power set of RR is:

Options

  1. A32
  2. B16
  3. C8
  4. D64

Correct answer

B. 16

Step-by-step solution

A={x:∣x∣<3,x∈Z}A={−2,−1,0,1,2}R={(x,y):y=∣x∣,x≠−1}R={(−2,2),(0,0),(1,1),(2,2)}\begin{aligned}&\mathrm{A}=\{x:|x| < 3, x \in Z\} \\ &\mathrm{A}=\{-2,-1,0,1,2\} \\ &\mathrm{R}=\{(x, y): y=|x|, x \neq-1\} \\ &\mathrm{R}=\{(-2,2),(0,0),(1,1),(2,2)\} \end{aligned}\mathrm{R}hasfourelementsNumberofelementsinthepowersetofhas four elements Number of elements in the power set of\mathrm{R}$ =2^4=16
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