Make a Venn Diagram that reflects a part of the following statement: “… we have left undone that which we ought to have done, and we have done that which we ought not to have done …

a. The following pair of concepts are related in some way and different in another.  Explain how the concepts are similar and how they are different:  GROUP BY / ORDER BY b. The following pair of concepts are related in some way and different in another.  Explain how the concepts are similar and how they are different: WHERE / HAVING

p.77, icon at Example 6 #1. The proposition (¬q^(p → q)) →¬p is a tautology, as the reader can check. It is the basis for the rule of inference modus tollens: ר קר Suppose we are given the propositions: “If the class finishes Chapter 2, then they have a quiz” and “The class does not have a quiz." Find a conclusion that can be drawn using modus tollens.

In the study of formal languages state-transition diagrams are often usedto visualize changes in a machine’s configuration as it acts on input. To visualize amachine’s configuration think of its parts: Commonly a finite set of states, a finiteinput alphabet Σ, Perhaps storage devices (a stack, input/output tapes). The states arepictured as named circles sometimes decorated with symbols to denote special states,e.g. start and final states. Changes in configuration are denoted by labeled edges andperhaps changes in storage.1. Describe how edges are labeled and their meaning for finite state machines.2. Describe how edges are labeled and their meaning for pushdown automata.3. Describe how edges are labeled and their meaning for Turing machines.