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.

Answer 1

R = [(x, y) : x, y ∈ Z, y = 2x − 4]
(a, $-$2) and (4, b²) ∈ R

$$\begin{gathered} \mathrm{So,}-2\; =\; 2(a)\; -4 \\ \Rightarrow 2=2a \\ \Rightarrow a=1 \end{gathered}$$

$$\begin{gathered} \mathrm{Also},b^2=2\left(4\right)-4 \\ \Rightarrow b^2=4 \\ \Rightarrow b=\pm 2 \end{gathered}$$

Thus, a =1 and b = $\pm 2$