Solve all questions.
Show all work.
You may use any of the Laws of Logical Equivalences and/or Logical Equivalences for Propositional Logic and
Predicate Logic.
For any law of logical equivalence that you use, please indicate the law or the
logical equivalence number.
(1.) Decide whether these statements makes sense (or is clearly true) or does not make sense (or is clearly false).
Explain your reasoning.
(a.) My logical proposition is a question that you must answer.
(b.) The United States intends to capture the terrorist, dead or alive.
(c.) When Sally is depressed, she listens to music. I saw her today listening to music, so she must have been depressed.
(d.) Now that I've studied logic, I can always determine the truth of any statement by making a truth table for it.
(e.) If all novels are books, then all books are novels.
(a.) Propositions are not questions. So, the statement does not make sense.
(b.) The statement makes sense because when the terrorist the statement is referring to is caught, he must be either dead or alive.
(c.) The statement does not make sense.
Sally listens to music when she is depressed, but the statement does not clearly state that this is the only time Sally listens to music.
(d.) The statement does not make sense.
A truth table displays each possible set of truth values for the propostions being considered, but does not always make a definitive conclusion about the propostion.
(e.) The statement does not make sense.
Not all books are novels.
Explain your reasoning.
(a.) My logical proposition is a question that you must answer.
(b.) The United States intends to capture the terrorist, dead or alive.
(c.) When Sally is depressed, she listens to music. I saw her today listening to music, so she must have been depressed.
(d.) Now that I've studied logic, I can always determine the truth of any statement by making a truth table for it.
(e.) If all novels are books, then all books are novels.
(a.) Propositions are not questions. So, the statement does not make sense.
(b.) The statement makes sense because when the terrorist the statement is referring to is caught, he must be either dead or alive.
(c.) The statement does not make sense.
Sally listens to music when she is depressed, but the statement does not clearly state that this is the only time Sally listens to music.
(d.) The statement does not make sense.
A truth table displays each possible set of truth values for the propostions being considered, but does not always make a definitive conclusion about the propostion.
(e.) The statement does not make sense.
Not all books are novels.
(2.) Which of the following is an:
(I.) Inclusive Disjunction
(II.) Exclusive Disjunction
A. An integer is either a positive number or a negative number.
B. Two lines are parallel or intersect at a point.
C. A non-zero number can be greater than or less than zero.
D. A quadrilateral can be a polygon with 4 sides or a polygon with 4 vertices.
E. Someone will read a book or a magazine the next time I go to the library.
F. The insurance covers a trip to the doctor's office or a trip to the emergency room.
G. The rules clearly state that chewing gum or eating food is not permitted.
H. Before the test, someone have the choice of studying or watching television.
I. Her favorite sport is tennis or golf.
J. He will eat supper at restaurant A or restaurant B.
K. For elective classes, she could take Spanish or Arabic.
Let us analyze each option: (based on the possibilities of only what we are given rather than all possibilities)
A. An integer is either a positive number or a negative number.
An integer cannot be both a positive number and a negative number.
Based on what we are given: this is an Exclusive OR
Based on all possibilities:
An integer can also be zero. Zero is neither a positive number nor a negative number.
B. Two lines are parallel or intersect at a point.
Based on what are given: this is an Exclusive OR because two lines will either not meet (parallel) or meet(intersect) at a point.
Two lines cannot meet, and meet at a point.
C. A non-zero number can be greater than or less than zero.
This is an Exclusive OR
A non-zero number is either greater than zero or less than zero. It cannot be both.
D. A quadrilateral can be a polygon with 4 sides or a polygon with 4 vertices.
Examples of quadrilaterals are: square, rectangle, rhombus, kite, parallelogram, trapezium
These are polygons with four sides and four vertices.
They have four sides.
They have four vertices.
They have four sides and four vertices.
This is an example of Inclusive OR
E. I will read a book or a magazine the next time I go to the library.
Technically speaking, magazine is a book. Be it as it may, one can read a book and a magazine at the same time.
One can read a book.
One can read a magazine.
One can read a book and a magazine simultaneously.
This is an example of Inclusive OR
F. My insurance covers a trip to the doctor's office or a trip to the emergency room.
The insurance can cover a trip to the doctor's office.
The insurance can also cover a trip to the emergency room.
The insurance can conver a trip to the doctor's office and a trip to the emergency room.
This is an example of Inclusive OR
The rules clearly state that chewing gum or eating food is not permitted.
This implies that chewing gum is not permitted.
Eating food is not permitted.
Chewing gum and eating food is not permitted.
This is an example of Inclusive OR
H. Before the test, someone have the choice of studying or watching television.
Someone can be studying.
Someone can be watching television.
However, someone cannot be studying and watching television simultaneously.
This is an example of Exclusive OR
I. Her favorite sport is tennis or golf.
Her favorite sport [emphasis on sport (not sports)] cannot be both tennis and golf. It has to be just one of them.
This is an example of Exclusive OR
J. He will eat supper at restaurant A or restaurant B.
He cannot eat supper at the two restaurants simultaneously. He will either eat at restaurant A or restaurant B but not both.
This is an example of Exclusive OR
K. For elective classes, she could take Spanish or Arabic.
She could take Spanish.
She could take Arabic.
She could take both Spanish and Arabic.
This is an example of Inclusive OR
(I.) Inclusive Disjunction
(II.) Exclusive Disjunction
A. An integer is either a positive number or a negative number.
B. Two lines are parallel or intersect at a point.
C. A non-zero number can be greater than or less than zero.
D. A quadrilateral can be a polygon with 4 sides or a polygon with 4 vertices.
E. Someone will read a book or a magazine the next time I go to the library.
F. The insurance covers a trip to the doctor's office or a trip to the emergency room.
G. The rules clearly state that chewing gum or eating food is not permitted.
H. Before the test, someone have the choice of studying or watching television.
I. Her favorite sport is tennis or golf.
J. He will eat supper at restaurant A or restaurant B.
K. For elective classes, she could take Spanish or Arabic.
Let us analyze each option: (based on the possibilities of only what we are given rather than all possibilities)
A. An integer is either a positive number or a negative number.
An integer cannot be both a positive number and a negative number.
Based on what we are given: this is an Exclusive OR
Based on all possibilities:
An integer can also be zero. Zero is neither a positive number nor a negative number.
B. Two lines are parallel or intersect at a point.
Based on what are given: this is an Exclusive OR because two lines will either not meet (parallel) or meet(intersect) at a point.
Two lines cannot meet, and meet at a point.
C. A non-zero number can be greater than or less than zero.
This is an Exclusive OR
A non-zero number is either greater than zero or less than zero. It cannot be both.
D. A quadrilateral can be a polygon with 4 sides or a polygon with 4 vertices.
Examples of quadrilaterals are: square, rectangle, rhombus, kite, parallelogram, trapezium
These are polygons with four sides and four vertices.
They have four sides.
They have four vertices.
They have four sides and four vertices.
This is an example of Inclusive OR
E. I will read a book or a magazine the next time I go to the library.
Technically speaking, magazine is a book. Be it as it may, one can read a book and a magazine at the same time.
One can read a book.
One can read a magazine.
One can read a book and a magazine simultaneously.
This is an example of Inclusive OR
F. My insurance covers a trip to the doctor's office or a trip to the emergency room.
The insurance can cover a trip to the doctor's office.
The insurance can also cover a trip to the emergency room.
The insurance can conver a trip to the doctor's office and a trip to the emergency room.
This is an example of Inclusive OR
The rules clearly state that chewing gum or eating food is not permitted.
This implies that chewing gum is not permitted.
Eating food is not permitted.
Chewing gum and eating food is not permitted.
This is an example of Inclusive OR
H. Before the test, someone have the choice of studying or watching television.
Someone can be studying.
Someone can be watching television.
However, someone cannot be studying and watching television simultaneously.
This is an example of Exclusive OR
I. Her favorite sport is tennis or golf.
Her favorite sport [emphasis on sport (not sports)] cannot be both tennis and golf. It has to be just one of them.
This is an example of Exclusive OR
J. He will eat supper at restaurant A or restaurant B.
He cannot eat supper at the two restaurants simultaneously. He will either eat at restaurant A or restaurant B but not both.
This is an example of Exclusive OR
K. For elective classes, she could take Spanish or Arabic.
She could take Spanish.
She could take Arabic.
She could take both Spanish and Arabic.
This is an example of Inclusive OR