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.

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).

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this

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