The deductive reasoning works at best when the statements used in the argument are true and the statements in the argument clearly follow from one another. The essence of deductive reasoning is drawing a conclusion from a given statement. If the given statement follows a conclusion from a hypothesis, then it is called valid deductive reasoning or the Law of Detachment.
Law of Detachment
If a⇒b is a true conditional statement and a is true, then b is true.
Example 3.16: If ∠A and ∠B are supplementary angles and m∠A =100° then ________.
Conclusion: m∠A+ m∠B=180° 100°+ m∠B=180° m∠B=80°
Example 3.17: All teachers are passionate. Royet is a teacher.
Conclusion: Therefore, Royet is passionate.
Example 3.18: All squares have …show more content…
A quadrilateral has four sides.
A rectangle is a quadrilateral.
Therefore, a rectangle has four sides.
II. Draw a conclusion from the given statements. Most students are irresponsible on their works.
Zaryna is a student. Every square is a rectangle.
Quadrilateral MINE is a square. Students who know Algebra is intelligent.
Royet is an intelligent student.
III. Write a conjecture based on the given information. Point A is between B and C. T, R, Y are collinear points. The number x is a perfect square.
IV. Solve this mystery. Lance reported to the police that criminals broke into his house last night and stole his laptop. Today, the laptop was traced at a lending station and some suspects were identified by the police. Can you identify the thief? The only suspects are Lance (the owner of the house), Jay-R (a gardener), Oliver (guest), and Rhex (a friend). The local police have gathered the following information: The break-in happened between 9:00-10:00 last night. Lance was sick that time. Jay-R has been visiting his ancestors in the province since a couple of month. Rhex’s and Oliver’s fingerprints were on the stolen laptop. Lance stayed in a friend’s house from 5:00-10:00 p.m. last
Law of Detachment
If a⇒b is a true conditional statement and a is true, then b is true.
Example 3.16: If ∠A and ∠B are supplementary angles and m∠A =100° then ________.
Conclusion: m∠A+ m∠B=180° 100°+ m∠B=180° m∠B=80°
Example 3.17: All teachers are passionate. Royet is a teacher.
Conclusion: Therefore, Royet is passionate.
Example 3.18: All squares have …show more content…
A quadrilateral has four sides.
A rectangle is a quadrilateral.
Therefore, a rectangle has four sides.
II. Draw a conclusion from the given statements. Most students are irresponsible on their works.
Zaryna is a student. Every square is a rectangle.
Quadrilateral MINE is a square. Students who know Algebra is intelligent.
Royet is an intelligent student.
III. Write a conjecture based on the given information. Point A is between B and C. T, R, Y are collinear points. The number x is a perfect square.
IV. Solve this mystery. Lance reported to the police that criminals broke into his house last night and stole his laptop. Today, the laptop was traced at a lending station and some suspects were identified by the police. Can you identify the thief? The only suspects are Lance (the owner of the house), Jay-R (a gardener), Oliver (guest), and Rhex (a friend). The local police have gathered the following information: The break-in happened between 9:00-10:00 last night. Lance was sick that time. Jay-R has been visiting his ancestors in the province since a couple of month. Rhex’s and Oliver’s fingerprints were on the stolen laptop. Lance stayed in a friend’s house from 5:00-10:00 p.m. last