Given the following: \( { }_{19}^{41} \mathrm{X},{ }_{19}^{39} \mathrm{X},{ }_{20}^{41} \mathrm{X} \), and \( { }_{18}^{39} \mathrm{X} \). Which are isotopes of each other? \( \begin{array}{l}{ }_{19}^{41} \mathrm{X},{ }_{19}^{39} \mathrm{X},{ }_{20}^{41} \mathrm{X} \text {, and }{ }_{18}^{39} \mathrm{X} \text { are isotopes of each other. } \\ { }_{19}^{41} \mathrm{X} \text { and }{ }_{20}^{41} \mathrm{X} \text { are isotopes of each other, and }{ }_{19}^{39} \mathrm{X} \text { and }{ }_{18}^{39} \mathrm{X} \text { are isotopes of each other. } \\ { }_{19}^{41} \mathrm{X} \text { and }{ }_{19}^{39} \mathrm{X} \text { are isotopes of each other. } \\ \text { None are isotopes of each other. }\end{array} \).

Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. In this case, \( { }_{19}^{41} \mathrm{X} \) and \( { }_{19}^{39} \mathrm{X} \) are isotopes of each other because they both have 19 protons (indicating they are the same element) but differ in their atomic mass due to a different number of neutrons. Similarly, \( { }_{18}^{39} \mathrm{X} \) cannot be an isotope of these two since it has only 18 protons, which means it is not the same element. On the flip side, \( { }_{20}^{41} \mathrm{X} \) represents a different element with 20 protons, thus it is not an isotope of the other two even though they share the same atomic mass. Essentially, only \( { }_{19}^{41} \mathrm{X} \) and \( { }_{19}^{39} \mathrm{X} \) are true isotopes of each other in this group.