Question

1. what does a formal proof need to have?

written in two - columns form.
justification for each step.
venn diagrams.
written in paragraph form.

Explanation:

A formal proof in geometry (for example) requires a justification for each step. This is because each statement in the proof must be supported by a theorem, postulate, definition, or given information. While proofs can be written in two - column, paragraph, or flow - chart form (so the form is not a strict requirement), and Venn diagrams are used in set theory (not a general requirement for formal proofs), the key element is having a reason (justification) for each step.

Answer:

Justification for each step.