![]() For example, the converse of the statement “if two lines are perpendicular, then they intersect” is “if two lines intersect, then they are perpendicular”, which is not always true. In general, the converse of a statement is not necessarily true, while the inverse of a statement is always true. An example of an inverse statement would be the inverse of the statement “if two lines are parallel, then they do not intersect”, which would be “if two lines are not parallel, then they intersect”. ![]() The difference between a converse statement and an inverse statement is that a converse statement switches the hypothesis and conclusion of a statement, while an inverse statement negates both the hypothesis and conclusion. What is the Difference Between a Converse Statement and an Inverse Statement? This is because two lines can intersect and still not be perpendicular. For example, the statement “if two lines are perpendicular, then they intersect” is true, but its converse “if two lines intersect, then they are perpendicular” is not always true. The converse of a statement is not necessarily true. Converse statements are a key concept in the study of geometry and are used to make deductions and draw inferences from geometric statements.Īn example of a converse statement in geometry is the statement “if two lines are parallel, then they do not intersect.” The converse of this statement is “if two lines do not intersect, then they are parallel.” In both cases, the hypothesis is that two lines do or do not intersect, and the conclusion is that the two lines are or are not parallel. In other words, the converse of a statement is a statement in which “B, then A” is true. The converse of a statement is the statement in which the hypothesis and conclusion have been switched. ![]() What is a Converse Statement in Geometry?Ī converse statement in geometry is a statement of the form “if A, then B” in which A is the hypothesis and B is the conclusion. For example, the converse of the statement “If two angles are congruent, then they are equal” is “If two angles are equal, then they are congruent.” It is formed by switching the hypothesis and the conclusion of the original statement. Then the law of syllogism tells us that if we turn of the water (p) then we don't get wet (r) must be true.A Converse Statement in Geometry is a statement that is the opposite of the original statement. If the water stops pouring (q) then we don't get wet any more (r). If we turn of the water (p), then the water will stop pouring (q). The law of syllogism tells us that if p → q and q → r then p → r is also true. This is called the law of detachment and is noted: This means that if p is true then q will also be true. If we call the first part p and the second part q then we know that p results in q. If we turn of the water in the shower, then the water will stop pouring. The most common patterns of reasoning are detachment and syllogism. If the conditional is true then the contrapositive is true.Ī pattern of reaoning is a true assumption if it always lead to a true conclusion. The contrapositive does always have the same truth value as the conditional. We could also negate a converse statement, this is called a contrapositive statement: if a population do not consist of 50% women then the population do not consist of 50% men. The inverse always has the same truth value as the converse. The inverse is not true juest because the conditional is true. ![]() If we negate both the hypothesis and the conclusion we get a inverse statement: if a population do not consist of 50% men then the population do not consist of 50% women. A conditional and its converse do not mean the same thing If both statements are true or if both statements are false then the converse is true. If we exchange the position of the hypothesis and the conclusion we get a converse statement: if a population consists of 50% women then 50% of the population must be men. Our conditional statement is: if a population consists of 50% men then 50% of the population must be women. If we re-arrange a conditional statement or change parts of it then we have what is called a related conditional. The example above would be false if it said "if you get good grades then you will not get into a good college". Hypotheses followed by a conclusion is called an If-then statement or a conditional statement.Ī conditional statement is false if hypothesis is true and the conclusion is false. The part after the "if": you get good grades - is called a hypotheses and the part after the "then" - you will get into a good college - is called a conclusion. If you get good grades then you will get into a good college. We will explain this by using an example. If we instead use facts, rules and definitions then it's called deductive reasoning. When we previously discussed inductive reasoning we based our reasoning on examples and on data from earlier events.
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |