Chap 0.5 Logic

p→q

p

q

Law of Detachment

p→q If it is raining, then the ground is wet.

p It is raining.

q The ground is wet.

Law of Detatchment

p→q

~q

~p

Law of Contrapositive

Law of Contrapositive

p→q If it is a dog, then it is a mammal.

~q It is not a mammal.

~p It is not a dog.

(p→q): If it is electric, then it needs a battery.

(q→r): If it needs a battery, then it must be charged.

(p→r): If it is electric, then it must be charged.

Law of Syllogism

Law of Syllogism

p→q

q→r

p→r

p ∨q

∼p

q

Law of Disjunctive Inference

p ∨q The door is open or the door is closed

∼p The door is not open
q Therefore, the door is closed

Law of Disjunctive Inference

p→q If it rains, the ground gets wet.

q The ground is wet.

p It rained.

Fallacy of the Converse

Fallacy of the Converse

p→q

q

p

p→q

~p

~q

Fallacy of the Inverse

Fallacy of the Inverse

p→q If it rains, the ground gets wet.

~p It is not raining.

~q Therefore, the ground is not wet.

Law of Syllogism

If you study hard, then you pass the class.

If you pass the class, then you earn your degree.

If you study hard, then you earn your degree.

Law of Contrapositive

If a shape is a square, then it has four sides

This shape does not have four side

This shape is not a square

Law of Disjunctive Inference

The keys are either in your pocket or on the table

The keys are not in your pocket

The keys are on the table

Fallacy of the Inverse

If you are a beagle, then you are a dog

You are not a beagle

You are not a dog

Law of Detatchment

If you score a goal, then your team earns a point

You just scored a goal

Your team earned a point.

Fallacy of the Converse

If you score a goal, then your team earns a point

Your team just earned a point

 YOU must have scored a goal.

What is the negation of the statement: "The triangle is right-angled"?

The triangle is not right-angled.

What is the negation of the statement: "All integers are even”

At least one integer is not even.

Which option correctly rewrites "All dogs are mammals" in If-Then form?

If it is a dog, then it is a mammal.

Which option correctly rewrites "3x + 5 = 11 If x = 2" as a conditional statement?

If x = 2, then 3x + 5 = 11.

Which two conditional statements make up the biconditional: "An angle is acute if and only if its measure is less than 90 degrees"?

Statement 1: If an angle is acute, then its measure is less than 90 degrees. Statement 2: If an angle's measure is less than 90 degrees, then it is acute.

Which two conditional statements form the biconditional: "A number is divisible by 2 if and only if it is an even number"?

Statement 1: If a number is divisible by 2, then it is an even number. Statement 2: If a number is an even number, then it is divisible by 2.

Which symbolic statement represents the converse of p → q?

q → p

Which symbolic statement represents the inverse of p → q?

~p → ~q

Which symbolic statement represents the contrapositive of p → q?

~q →~p

When both p and q are true

Under what condition is the conjunction p and q TRUE?

Under what condition is the disjunction p or q FALSE?

When both p and q are false

Every car my family has owned made it past 200,000 miles without major repairs. Therefore, all cars made by that manufacturer are extremely reliable. What type of reasoning is used here?

Inductive

To graduate from high school, a student must complete 4 years of English credit. Jordan is graduating from high school today. Therefore, Jordan has completed 4 years of English credit. What type of reasoning is used here?

Deductive

A scientist tests 500 samples of water from a lake and finds high levels of acidity in every sample. The scientist concludes that the entire lake is acidic. What type of reasoning is used here?

Inductive

In order to vote in a national election, a citizen must be at least 18 years old. Maya is voting in the national election today. Therefore, Maya is at least 18 years old. What type of reasoning is used here?

Deductive