Which of the following are accepted without proof in a logical system? Check all that apply.?

Question

Which of the following are accepted without proof in a logical system? Check all that apply.

A. theorems
B. postulates
C. corollaries
D. conjectures

Answer 1

Of the four mentioned, only Postulates are accepted as true without proof.

Euclid had only five Postulates which pertain to Geometry.
They were:
1. It is possible to draw one and only one straight line between any two points.
2. It is possible to extend a finite straight line segment indefinitely.
3. It is possible to describe a circle with any given center and any given radius
4 All right angles are equal
5. If two lines are crossed by a third line (transversal) such that the interior angles on the same side of the transversal have a sum of less than two right angles, then the two lines will eventually intersect on the same side of the transversal.

In today's Geometry classes, many theorems proved by Euclid using only the above postulates and arithmetic/algebraic axioms are now called postulates. Sad that math has degenerated so much oive the 2000 years since Euclid wrote his Elements of Geometry.

Answer 2

sure, that's real. many individuals have presented this paradox at countless situations, yet I shop getting the customarily occurring evasions like "god is basically too mysterious to comprehend" etc, or the in call for "god exists outdoors time and area" neglecting that which skill he won't be in a position of be a piece of any limited timeline reference physique, and so no one even recognizes the actual logical paradox on the coronary heart of the declare. It does spotlight that good judgment isn't probable the stable factor of the claimants. Omnipotence is a nonsense besides for many different reasons too e.g. an all-powerful god is a factor of the 'each little thing' that's the universe, so won't be in a position of be any much less limited than that universe. If he's all-powerful he's without constraint, so the universe must be without constraint. which skill it has no actual nature, so existence itself has no nature. that should point there is not any distinction between existence and non-existence, that's additionally a paradox. for this reason any god that exists must be limited by skill of the certainty hat he exists, so won't be in a position of be unconstrained i.e. all-powerful.

Answer 3

B.
Something assumed without proof as being self-evident or generally accepted, especially when used as a basis for an argument. In mathematics, this is an axiom.

Answer 4

b

postulates or axioms are accepted without proof. Definitions as well.

Answer 5

Apex-Axioms,postulates,and common notions are the correct answer!!

Answer 6

axioms and postulates
-APEX