Question

1. what does a formal proof need to have?

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

Explanation:

A formal proof must have a justification for each step. This is because a proof is a logical sequence of statements, and each statement must be supported by a valid reason (such as a definition, axiom, theorem, or previously proven result). The form (paragraph, two - column) is just a way of presenting the proof. Venn diagrams are used for visualizing set - related concepts and are not a requirement for a formal proof.

Answer:

Justification for each step.