Question

Match the justifications for each step in order to complete the proof.

A. Substitution
B. Induction
C. Contradiction
D. Direct Proof

Answer 1

The justifications for each step in completing a proof are substitution, induction, contradiction, and direct proof.

Step-by-step explanation:

The justifications for each step in completing a proof are as follows:

1. Substitution: In this step, we replace variables or terms with equivalent values or expressions. This is useful to simplify equations or make calculations.
2. Induction: Induction is used to prove statements that hold true for all natural numbers. It involves proving a base case and then showing that the statement holds for an arbitrary natural number, assuming it holds for the previous natural number.
3. Contradiction: Contradiction is a proof technique that involves assuming the opposite of what we want to prove and showing that it leads to a contradiction. This implies that the original claim must be true.
4. Direct Proof: In a direct proof, we use logical steps to show that the hypothesis or assumption directly implies the conclusion. This is a straightforward and direct way of proving a statement.