Q:

What is the law of detachment in geometry?

A:

Quick Answer

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.

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Full 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:

  • All mammals have fur
  • All cats have fur
  • All cats must be mammals

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.

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Related Questions

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    What is a conditional statement in geometry?

    A:

    A conditional statement is an "if-then" statement used in geometry to relate a particular hypothesis to its conclusion. An arrow originating at the hypothesis, denoted by p, and pointing at the conclusion, denoted by q, represents a conditional statement. A conditional statement is read as, "if p then q."

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    What are the converse, invere and contrapositive in geometry?

    A:

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    What are some examples of acute angles found in real life?

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    What is sacred geometry?

    A:

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