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  4. A relation on the set A = x: |x| < 3, x ∈ Z , where Z is the set of integers is defined by R = (x, y): y = |x|, x ≠ - 1. Then the number of elements in the power set of R is:

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

Sets

Solution:

A = {x : |x| < 3, x $\in$ Z }
A = {-2, - 1, 0, 1, 2}
R = {(x, y) : y = |x|, x $\neq$ -1}
R = {(-2, 2), (0, 0), (1, 1), (2, 2)}
R has four elements
Number of elements in the power set of $R = 2^4 = 16$