Minimum symbol precedence

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If you find $$(t-s)\alpha \wedge 1$$ for $t,s,\alpha,\beta \in \mathbb{R}$ then what symbol has the precedence? Do I need to calculate first $(\alpha \wedge 1)$ and then $(t-s)(\alpha \wedge 1)$ or $(t-s)\alpha$ and then calculate the minimum $(t-s)\alpha \wedge 1$ ?

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There is no right or wrong answer - as it stands the notation is ambiguous. That being said, based off your question here my guess is that $$(t-s) \alpha \, \wedge \, 1 $$ means $$((t-s) \alpha )\, \wedge \, 1 $$ i.e. $$\min \{ (t-s)\alpha,1 \}. $$