Statements
Symbols
Valid
Counterexamples
Laws
100
The converse of "If I win, then you lose."
What is "If you lose, then I win."
100
Given: π β ~π.
What is the converse of this statement?
What is ~πβπ
100
Is this valid? AND by what law?
All squares are rectangles.
ABCD is a square.
Therefore, ABCD is a rectangle
Valid, Law of Detachment
100
Provide a counterexample:
If you are eating a red fruit, then you are eating an apple.
pomegranate, strawberry, raspberry, cherry, etc
100
What law is this?
If the geometry students score 100% on the test, the teacher will dye her hair. The geometry students scored 100% on the test.
Law of Detachment
200
The Contrapositive of, "A six-sided polygon is a hexagon."
What is: If it is not a hexagon, then it is not a six-sided figure.
200
Given: π β ~π.
What is the inverse of this statement?
What is ~π β π
200
Is this valid?
All squares are rectangles. ABCD is a rectangle. Therefore, ABCD is a square
Not valid.
200
Provide a counterexample
If π₯ + 4 > 10, then x is greater than 8.
6.1, 6.5, 7, 7.3, 7.555555, 7.9999
200
Apply the law of contrapositive to provide a valid conclusion.
If Sarah gets an A in the class, then she will not have to take the final exam.
Sarah had to take the final exam, therefore Sarah didn't get an A in the class.
300
What is the inverse of :
"If they make me run the pacer, then I will try to break my ankle before it starts."
If they don't make me run the pacer, I will not try to break my ankle before it starts.
300
Suppose the symbolic statements π β π and π β π are true. Determine two other statements that must also be true.
π β π , ~c β ~a
300
Is this valid? What law?
If you wear school colors, then you have school spirit.
If you have school spirit, then you feel great.
If you wear school colors, then you feel great.
Yes! Law of Syllogism
300
tea with honey
300
What law is this?
If you have exact change, then you can use the snack machine. And you cannot use the snack machine then you donβt have the exact change.
Law of Contrapositive
400
Write this as a biconditional phrase:
if the grass is green, then it rained.
The grass is green iff it rained.
400
What is the symbol AND the abbreviation we use for biconditional
What is iff and β
400
What goes in the blank to make this statement valid? And what Law did you use?
"If Jamal misses practice, then he is not allowed to play in tomorrowβs game.
Jamal played in the game.
Therefore________________"
Jamal didn't miss practice. Law of Contrapositive
400
All numbers greater than 20 are divisible by itself, 1, and at least 2 other number.
Any prime number greater than 20
400
What law is this?
None of them, it's invalid.
500
Find the biconditional phrase by looking at the conditional and converse statement to figure out if it is valid:
If it is a circle, then it doesn't have angles.
Valid or invalid?
Valid.
Conditional: True
Converse: True
Biconditional: has to be true
500
Give an example using the symbol therefore in a complete symbolic language
500
Determine if this argument is valid. If so, indicate the law(s) of logic used.
If a figure has three sides, then it is a triangle.
If a figure is a triangle, then the sum of the interior angles is 180Β°.
Therefore, if the sum of the interior angles is not 180 degrees, then the figure does not have three sides.
Valid. By law of contraposition and law of syllogism
500
The sum of two numbers is always more than the greater number.
Counter example: -2 + -3 = -5
500
Tall boys are always brilliant.
Chris is always brilliant.
Therefore: _______________
Therefore nothing! There's no logical conclusion.