 Interestingly, each left-continuous t-norm determines a suitable choice for implication. Indeed, it is known that a t-norm \(\ast\) is left-continuous if, and only if, there is a unique binary operation \(\Rightarrow_\ast\) on \([0,1]\) satisfying the so-called residuation condition:   \[ x \ast y \leq z\ \text{ if and only if, }\ x \leq y \Rightarrow_\ast z. \]    The function \(\Rightarrow_\ast\) is known as residuum of \(\ast\), and it can be shown that \(x \Rightarrow_\ast y = \max\{z \mid x \ast z \leq y\}\). The residua of the three mentioned prominent t-norms are: \(x \Rightarrow_\min y = 1\) if \(x\leq y\) and \(y\) otherwise; \(x \Rightarrow_\cdot y = 1\) if \(x\leq y\) and \(\frac{y}{x}\) otherwise; and \(x \Rightarrow_{Ł} y = \min\{1, 1 - x+y\}\).