**Notation**              | **Meaning**                           | **Formula**        |:-------------------------|:--------------------------------------|:-------------------|${}_tp_{xy}$              | Probability $(x)$ and $(y)$ are both alive in $t$ years | $\Pr(T_{xy}>t)$ |${}_tq_{xy}$              | Probability $(x)$ and $(y)$ are **not** both alive in $t$ years | $\Pr(T_{xy}\le t)$ |${}_{u\vert t}q_{xy}$     | Probability $(x)$ and $(y)$ are both alive in $u$ years but not in $u+t$ years | $\Pr(u < T_{xy}\le u+t)$ |${}_tq_{xy}^{\, 1}$       | Probability $(x)$ dies before $(y)$  and within $t$ years | $\Pr(T_{x}\le t \text{ and } T_x < T_y)$ |${}_tq_{xy}^{\, 2}$       | Probability $(x)$ dies after $(y)$  and within $t$ years | $\Pr(T_y < T_{x}\le t)$ |${}_tp_{\overline{xy}}$   | Probability at least one of $(x)$ and $(y)$ is alive in $t$ years | $\Pr(T_{\overline{xy}}>t)$ |${}_tq_{\overline{xy}}$   | Probability both $(x)$ and $(y)$ is dead in $t$ years | $\Pr(T_{\overline{xy}} \le t)$ |

**Notation**              | **Meaning**                           | **Formula**        |:-------------------------|:--------------------------------------|:-------------------|${}_tp_{xy}$              | Probability $(x)$ and $(y)$ are both alive in $t$ years | $\Pr(T_{xy}>t)$ |${}_tq_{xy}$              | Probability $(x)$ and $(y)$ are **not** both alive in $t$ years | $\Pr(T_{xy}\le t)$ |${}_{u\vert t}q_{xy}$     | Probability $(x)$ and $(y)$ are both alive in $u$ years but not in $u+t$ years | $\Pr(u < T_{xy}\le u+t)$ |${}_tq_{xy}^{\, 1}$       | Probability $(x)$ dies before $(y)$  and within $t$ years | $\Pr(T_{x}\le t \text{ and } T_x<T_y)$ |${}_tq_{xy}^{\, 2}$       | Probability $(x)$ dies after $(y)$  and within $t$ years | $\Pr(T_y < T_{x}\le t)$ |${}_tp_{\overline{xy}}$   | Probability at least one of $(x)$ and $(y)$ is alive in $t$ years | $\Pr(T_{\overline{xy}}>t)$ |${}_tq_{\overline{xy}}$   | Probability both $(x)$ and $(y)$ is dead in $t$ years | $\Pr(T_{\overline{xy}} \le t)$ |