1. **Problem statement:** Given points $A(1, -3, 2)$, $B(2, 5, 3)$, and $C(4, -3, 5)$ in space $Oxyz$, verify if $I(3, 1, -4)$ is the midpoint of segment $BC$. 2. **Formula for midpoint:** The midpoint $I$ of segment $BC$ is given by $$I = \left(\frac{x_B + x_C}{2}, \frac{y_B + y_C}{2}, \frac{z_B + z_C}{2}\right)$$ 3. **Calculate midpoint coordinates:** $$x_I = \frac{2 + 4}{2} = 3$$ $$y_I = \frac{5 + (-3)}{2} = \frac{2}{2} = 1$$ $$z_I = \frac{3 + 5}{2} = \frac{8}{2} = 4$$ 4. **Compare with given point $I(3, 1, -4)$:** The $x$ and $y$ coordinates match, but $z$ coordinate is $4$ from calculation, while given is $-4$. 5. **Conclusion:** Since $z$ coordinate does not match, $I(3, 1, -4)$ is **not** the midpoint of $BC$. **Final answer:** The statement a) is **False**.