Question 84
For a non-empty set $\mathcal{T}$ denote by $p(\mathcal{T})$ the product of all elements of $\mathcal{T}$. Does there exist a set $\mathcal{T}$ of 2021 elements such that for any $a \in \mathcal{T}$ one has that $p(\mathcal{T}) - a$ is an odd integer. Consider two cases:
1. All elements of $\mathcal{T}$ are irrational numbers?
2. At least one element of $\mathcal{T}$ is a rational number?
1. All elements of $\mathcal{T}$ are irrational numbers?
2. At least one element of $\mathcal{T}$ is a rational number?