Give me a reason
Definitions
True, Valid, and Sound?
Define it
Law of Reason
100
If 3x = 12, then x = 4.
Multiplication Property of Equality
100
Two angles that have a sum of 180⁰
Supplementary angles
100
Premise 1: All men are mortal.
Premise 2: Socrates is a man.
Conclusion: Socrates is mortal.
True, valid, and sound
100
Type of reasoning that draws a conclusion after observing patterns in several examples
Inductive reasoning
100
If a number is even, then it is divisible by 2.
15 is not divisible by 2.
Therefore, 15 is not even.
Modus tollens
200
If 27⁰ = x, then x = 27⁰
Symmetric Property of Equality
200
Two angles that have a sum of 90⁰
Complementary angles
200
Premise 1: All birds are reptiles.
Premise 2: A sparrow is a bird.
Conclusion: A sparrow is a reptile.
Valid (the conclusion follows logically), but unsound (Premise 1 is false).
200
Given p → q, the ___ of the statement is q → p.
Converse
200
If you pass your driver′ s test, you get your license. You passed your driver′ s test.
You get your license.
Modus ponens
300
If AB = CD, CD = EF
Then AB = EF
Substitution or Transitive Property of Equality
300
Nonadjacent angles of two intersecting lines
Vertical angles
300
Premise 1: The sky is blue.
Premise 2: Water boils at 100°C.
Conclusion: Therefore, the grass is green.
Argument is invalid. Premises do not support the conclusion. Unsound.
300
Given p → q, the ___ of the statement is not p → not q.
Inverse
300
If line l ∥ line m and line m ∥ line n,
then line l ∥ line n.
Transitivity
400
If angle A is congruent to angle B and angle A = 50⁰, then angle B = 50⁰.
Definition of congruent angles.
400
Two angles that share a common ray and endpoint but no common interior points
Adjacent angles
400
Premise 1: The Constitution states that anyone who has ever owned a cat is legally disqualified from running for President of the United States.
Premise 2: Candidate Jones has owned three cats in his lifetime.
Conclusion: Therefore, Candidate Jones is legally disqualified from running for President of the United States.
Valid but premise 1 is untrue; therefore, the argument is unsound
400
Given p → q, the ___ of the statement is
not q → not p.
Contrapositive
400
If the plant gets enough sunlight, then it will grow tall.
The plant did not grow tall.
Therefore, it did not get enough sunlight.
Modus tollens
500
Angle Addition Postulate
500
Two angles that have the same measure
Congruent angles
500
Premise 1: Senator Smith served honorably as a pilot in the United States Air Force.
Premise 2: The federal highway budget increased by four percent last fiscal year.
Conclusion: Senator Smith's proposed corporate tax reform bill will lower the national deficit.
True premises, Invalid, Unsound
500
The biconditional p ↔ q is true when
(p → q) Λ ______.
q → p
500
If a triangle is equilateral, then all three of its angles measure 60°.
Triangle ABC is equilateral.
Therefore, all three angles of triangle ABC measure 60°.
Modus ponens