Chapter 12.2, Problem 16E

Show that $\{\downarrow \}$ is functionally complete using Exercise 15.

15. Show that

a) $\bar{x}=x\downarrow x$ .

b) $xy=\left(x\downarrow x\right)\downarrow \left(y\downarrow y\right)$ .

c) $x+y=\left(x\downarrow y\right)\downarrow \left(x\downarrow y\right)$ .