Which term best describes the statement given below if XY and YZ then X Z?

Which term best describes the statement given below if XY and YZ then X Z?

I think the answer is ,syllogism.

Which term best describes the statement given below if a B and B C then a C?

syllogism

Which best describes the meaning of the term theorem?

In other words, a theorem is a conclusion, statement, or result that has been proved to be true by deductive reasoning, that is to say, by going through a logical process that starts with a general statement (hypothesis) and follows several steps (such as formulas and operations) in order to reach a specific, logical …

Which of the following can be used to explain a statement in a geometric proof?

Definition, Postulate, Corollary, and Theorem can all be used to explain statements in geometric proofs.

What can be used to explain a proof?

A-theorem ; B-corollary ; C-Postulate ; and E-Definition. Explanation: In a proof, we are tasked with proving one statement using other information that has already been proven. Theorems are statements that have already been proven, and are used to prove other statements.

Is a postulate a conjecture that has been proven?

Postulates are accepted as true without proof. A logical argument in which each statement you make is supported by a statement that is accepted as true. An informal proof written in the form of a paragraph that explains why a conjecture for a given situation is true.

How will you determine if the conjecture is true?

To prove a conjecture is true, you must prove it true for all cases. It only takes ONE false example to show that a conjecture is NOT true. This false example is a COUNTEREXAMPLE. Find a counterexample to show that each conjecture is false.

Can postulates always be proven true?

A postulate (also sometimes called an axiom) is a statement that is agreed by everyone to be correct. Postulates themselves cannot be proven, but since they are usually self-evident, their acceptance is not a problem. Here is a good example of a postulate (given by Euclid in his studies about geometry).

What is a conjecture that has been proven?

Theorem. A statement or conjecture has been proven, and can be used as a reason to justify statements in other proofs.

Does a counterexample always disprove a conjecture?

1 Answer. A counterexample always disproves conjectures. A conjecture will suppose that something is true for different cases, but if you find an example where it is not, the conjecture must be modified to not include a particular case or rejected.

Why can a conjecture be true or false?

A conjecture is an “educated guess” that is based on examples in a pattern. However, no number of examples can actually prove a conjecture. It is always possible that the next example would show that the conjecture is false. A counterexample is an example that disproves a conjecture.

What is the difference between law and Theorem?

1 Answer. Theorems are results proven from axioms, more specifically those of mathematical logic and the systems in question. Laws usually refer to axioms themselves, but can also refer to well-established and common formulas such as the law of sines and the law of cosines, which really are theorems.

What is another word for Theorem?

In this page you can discover 30 synonyms, antonyms, idiomatic expressions, and related words for theorem, like: theory, thesis, dictum, assumption, doctrine, hypothesis, axiom, belief, law, principle and fact.

What is the difference between definition and Theorem?

A theorem provides a sufficient condition for some fact to hold, while a definition describes the object in a necessary and sufficient way. As a more clear example, we define a right angle as having the measure of π/2.

What does Lemma mean in math?

In mathematics, informal logic and argument mapping, a lemma (plural lemmas or lemmata) is a generally minor, proven proposition which is used as a stepping stone to a larger result.

Do we prove theorems?

A theorem is hence a logical consequence of the axioms, with a proof of the theorem being a logical argument which establishes its truth through the inference rules of a deductive system. As a result, the proof of a theorem is often interpreted as justification of the truth of the theorem statement.

What is Lemma and Corollary?

Lemma: A true statement used in proving other true statements (that is, a less important theorem that is helpful in the proof of other results). • Corollary: A true statment that is a simple deduction from a theorem or proposition. • Proof: The explanation of why a statement is true.

Can a lemma have a corollary?

Lemma — a minor result whose sole purpose is to help in proving a theorem. Corollary — a result in which the (usually short) proof relies heavily on a given theorem (we often say that “this is a corollary of Theorem A”).

Do axioms Need proof?

Unfortunately you can’t prove something using nothing. You need at least a few building blocks to start with, and these are called Axioms. Mathematicians assume that axioms are true without being able to prove them. If there are too few axioms, you can prove very little and mathematics would not be very interesting.

What is Euclid full name?

Euclid, Greek Eukleides, (flourished c. 300 bce, Alexandria, Egypt), the most prominent mathematician of Greco-Roman antiquity, best known for his treatise on geometry, the Elements.

Who first used geometry?

Ancient Babylonians ‘first to use geometry’ Sophisticated geometry – the branch of mathematics that deals with shapes – was being used at least 1,400 years earlier than previously thought, a study suggests.