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Homework Statement
Context: Both [itex]\sigma[/itex] and [itex]\tau[/itex] are stopping times in the filtered probability space [itex](\Omega,\mathscr{F},\{\mathscr{F}_t\}_{t\in [0,\infty)},P)[/itex].
Question: Why is it the case that [itex]\{min(\sigma,\tau) \leq t\} = \{\sigma \leq t\}\cup \{\tau \leq t\}[/itex]?
The Attempt at a Solution
I don't know why.