The relation on the set $A= \{x:|x| <3, x ∈ Z\}$ is defined by $R= \{(x, y): y=|x|, x ≠ -1\}$. Then the number of elements in the power set of R is _____.

16

We have, $A=\{x:|x|<3,x∈Z\}=\{-2, -1, 0, 1, 2\}$ and $R=\{(x, y): y = |x|, x ≠-1\}$ $R=\{(-2,2), (0, 0), (1, 1), (2, 2)\}$ Clearly, R has four elements. So, the number of elements in power set of R is $2^4 = 16$.