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MAT 243 test 2 with verified solutions 2025
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MAT 243 test 2 with verified solutions 2025
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MAT 243 test 2 with verifiedsolutions 2025
Informal proofs - answer Shows that a particular
mathematical result is correct
Math zoo - answer Made out of axioms, postulates, and
definitions
Math results - answer Consist of lemmas, propositions,
theorems, and corollaries
Lemmas - answer Small proofs that are needed for a
larger theorem or proposition
Proposition - answer A proof that isn't important enough
to be a theorem
Theorem - answer A major proof in mathematics, take the
form of "if premise... then... conclusion"
Corollary - answer a proposition that follows from one
already proven
Conjectures - answer A theory that can either be proved to
be a theorem or irrelevant
, Direct proofs - answer A type of proof where premises are
assumed to be true then use those along with previously
known knowledge to prove the theorem
Indirect proof - answer Prove that another statement
related to the original works, can be through contradiction
or contraposition
proof by contraposition - answer If proving if p then q, the
proof by contraposition would be proving if not q then p
Proof by contradiction - answer If proving if p then q, then
proof by contradiction would be p and not q being a
contradiction
Definition of rational number - answer If it can
represented by 2 integers m and n where m/n and n
Set - answer Unordered collection of distinguishable
objects
Element - answer A single member of the set (may be a
set itself)
Cardinality of a set - answer The number of elements in a
set, can be represented by c(S), n(S), or |S| where S is the
set in question
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