Exercise 4 Page 477

Let's list some advantages and disadvantages of each type of representation.

Flowcharts Proofs

Advantage (1): Flowcharts provide a visual representation of a proof, which is appealing.

Advantage (2): Whenever we combine two statements into one — for example, by using the Substitution Property of Equality — this is explicitly shown using two boxes. This makes it clearer how we arrived at that particular statement.

Disadvantage (1): Longer proofs can be hard to draw, as flowcharts require a lot of space.

Disadvantage (2): Flowcharts are time consuming to make.

Two-Column Proof

Advantage: Two-column proofs are a more organized and less time-consuming way to write proofs, especially if they are long.

Disadvantage (1): These are somewhat boring to look at and generally require more attention from the reader to understand.

Disadvantage (2): Compared to a flowchart, it requires the reader to connect two or more ideas that lead to another statement.