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# Exercise 95 - Chapter 2

edited June 2018

1) What is $$\bigvee \emptyset$$, which we generally denote $$0$$, in the case

a. $$\mathcal{V} = \textbf{Bool} = ( B , \le, true, \wedge )$$?

b. $$\mathcal{V} = \textbf{Cost} = ([0, \infty], \ge, 0, +)$$?

2) What is the join $$x \vee y$$ in the case

a. $$\mathcal{V} = \textbf{Bool}$$, and $$x, y \in \mathbb{B}$$ are booleans?

b. $$\mathcal{V} = \textbf{Cost}$$, and $$x, y \in [0, \infty]$$ are distances.

1. a) $$\mathrm{false}$$ b) $$\infty$$
2. a) $$x$$ inclusive or $$y$$, usually denoted $$x\vee y$$. b) $$\mathrm{min}(x,y)$$
Comment Source:1. a) \$$\mathrm{false}\$$ b) \$$\infty\$$ 2. a) \$$x\$$ inclusive or \$$y\$$, usually denoted \$$x\vee y\$$. b) \$$\mathrm{min}(x,y)\$$