Logic Exam 3

Since London is north of Paris and south of Edinburgh, it follows that Paris is south of Edinburgh.

Valid

The longest river in South America is the Amazon, and the Amazon flows through Brazil. Therefore, the longest river in South America flows through Brazil.

Valid 

The Empire State Building is taller than the Statue of Liberty, and the Statue of Liberty is taller than the Eiffel Tower. Therefore, the Empire State Building is taller than the Eiffel Tower.

Valid

Chicago is a city in Michigan and Michigan is part of the United States. Therefore, Chicago is a city in the United States

Valid

If Queen Elizabeth was born in Los Angeles, then she is a California native. Queen Elizabeth is not a California native. Therefore, Queen Elizabeth was not born in Los Angeles.

Valid 

All physicians are individuals who have earned degrees in political science, and some lawyers are physicians. Therefore, some lawyers are persons who have earned degrees in political science.

Valid 

P → Q english translations 

a. “If P then Q” 

b. Q if P

c. P only if Q

d. Provided P, Q

e. Q provided P

P → Q is equal to

~P V Q

P ←> Q

“If and only if”, “just in case”

P ←> is equal to

(P → Q) and (Q → P)

P → Q Logical Equivalences 

a. ~Q → ~P 

b. ~P V Q