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.
The "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 MoreStudying geometry helps students improve logic, problem solving and deductive reasoning skills. The study of geometry provides many benefits, and unlike some other complex mathematical disciplines, geometry has many practical and daily applications. It is used in art, engineering, sports, cars, architecture and much more.
Full Answer >A point in geometry is the exact position or location on a plane surface, according to Math Open Reference. Points are typically displayed as dots, and they are given upper case letters for a name to make them easy to identify.
Full Answer >Geometry is essential for applied mathematics, and it is used in architecture and engineering fields. Its development was crucial in the development of modern mathematics. It can also make abstract mathematical concepts more clear.
Full Answer >The converse in geometry applies to a conditional statement. In a conditional statement, the words "if" and "then" are used to show assumptions and conclusions that are to be arrived at using logical reasoning. This is often used in theorems and problems involving proofs in geometry.
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