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Question
Let R = [(x, y) : x, y ∈ Z, y = 2x − 4]. If (a, -2) and (4, b2) ∈ R, then write the values of a and b.
Solution
R = [(x, y) : x, y ∈ Z, y = 2x − 4]
(a, -2) and (4, b2) ∈ R
\[So, - 2 = 2(a) -4 \]
\[ \Rightarrow 2 = 2a \]
\[ \Rightarrow a = 1\]
\[Also, b^2 = 2\left( 4 \right) - 4\]
\[ \Rightarrow b^2 = 4\]
\[ \Rightarrow b = \pm 2\]
Thus, a =1 and b =\[\pm 2 \]
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