Question

Match each of 1 -6 with its appropriate definition from the list A - F below.

1. Axiom
2. Corollary
3. Contradiction
4. Tautology
5. Theorem
6. Lemma

a. An elementary mathematical truth that is assumed self-evident and not in need of proof.
b. A theorem that is an immediate consequence (and perhaps special case) of another theorem.
c. A proposition that is always false.
d. A proposition that is always true.
e. An important true mathematical statements.
f. A theorem that is needed as a stepping stone to prove a greater theorem.

Answer 1

Answer:

1. Axiom

Appropriate definition: An elementary mathematical truth that is assumed self-evident and not in need of proof (a).

2. Corollary

Appropriate definition: A theorem that is an immediate consequence (and perhaps special case) of another theorem (b).

3. Contradiction

Appropriate definition: A proposition that is always false (c).

4. Tautology

Appropriate definition: A proposition that is always true (d).

5. Theorem

Appropriate definition: An important true mathematical statements (e).

6. Lemma

Appropriate definition: A theorem that is needed as a stepping stone to prove a greater theorem (f).