Suppose someone plans to write an indirect proof of the conditional. Write a correct first sentence of the indirect proof.
If , then .
The correct first sentence would be “Assume that .”
The indirect proof is based on the classical notion that any given sentence, such as the conclusion, must be either true or false. The Indirect proof is done by assuming the premises to be true and the conclusion to be false and deriving a contradiction.
Consider the statement.
If then .
If someone wants to write an indirect proof for this statement then there is a need to write a correct first sentence of this indirect proof assuming the conclusion of the proof is not true.
The correct first sentence of the indirect proof is, Assume that .
Therefore, the correct first sentence of this indirect proof is “Assume that .”
Arrange sentences (a)-(e) in an order that completes an indirect proof of the following statement: In a plane, two lines perpendicular to a third line are parallel to each other.
Given: Lines a, b and t lie in a plane;
(a) Then a intersects b in some point Z.
(b) But this contradicts the theorem which says that there is exactly one line perpendicular to a given line through a point outside the line.
(c) It is false that a is not parallel to b, and it follows that
(d) Assume temporarily that a is not parallel to b.
(e) Then there are two lines through Z and perpendicular to t.
94% of StudySmarter users get better grades.Sign up for free