In geometry, the law of detachment is a form of deductive reasoning in which two premises in relation to the same subject are examined to come to a reasonable conclusion. This law considers a hypothesis made with regard to a statement and uses deductive reasoning to find a true answer.
Know MoreThe "if" part of the law of deductive reasoning is always a hypothesis or a reasoned guess. The statement made after "then" is the conclusion. This is also referred to as a conditional statement. The hypothesis must be proven to be true in order for the conclusion to be true as well. Another example of the law of deductive reasoning would be:
If the conclusion is false and the hypothesis is true in a conditional statement, then the conditional statement itself is false. A converse statement in the law of detachment happens when the hypothesis and the conditional statement are reversed. In the given example, the conclusion that all cats must be mammals would remain true.
Learn more about GeometrySpherical geometry is the branch of mathematics that deals with figures placed on the surface of a sphere. It can also be defined as a three-dimensional view of more traditional planar geometry; although, there are numerous differences between the planar and spherical subsets of geometrical study. Some of the basic tenets of planar geometry don't carry over to spherical geometry because it deals with different mathematical concepts.
Full Answer >The law of syllogism in geometry states that "if p, then q," and "if q then r." It’s also possible to derive a third statement that "if p, then r." The “if-then” statement applies to the law of syllogism to aid in deductive reasoning.
Full Answer >Euclid of Alexandria is called the Father of Geometry. He received his education at Plato's Academy in Greece and moved to Egypt to teach. He taught during the reign of Ptolemy I Soter, the first Macedonian ruler. Euclidian geometry has been taught in schools for a long time.
Full Answer >Geometry is defined as the area of mathematics dealing with points, lines, shapes and space. Geometry is important because the world is made up of different shapes and spaces. It is broken into plane geometry, flat shapes like lines, circles and triangles, and solid geometry, solid shapes like spheres and cubes.
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