Chapter 1.1 - 1.3: Logic and Proofs

Which of these is a proposition? A. Aristotle was born in norther Greece. B. Will you be coming to the party? C. x + 3 = 7 D. Go to bed!

A. Aristotle was born in norther Greece.

Consider the English sentence "If the exam is open book, then it will be hard." Converse

If the exam is hard, then it will be open book.

Consider the English sentence "If the exam is open book, then it will be hard." Contrapositive

If the exam is not hard, then it will be closed book.

Consider the English sentence "If the exam is open book, then it will be hard." Inverse

If the exam is not open book, then it will not be hard.

Consider the English sentence "If the exam is open book, then it will be hard." original implication

The exam being open book is sufficient for it being hard.

Which of the following English sentences represents the meaning of p->q where p is "The toy is lightweight" and q is "The toy floats"?

The toy floats when it is lightweight. A sufficient condition for the toy floating is that it is lightweight. The toy floating follows from it being lightweight.

It will not snow tomorrow, and it will be cold.

The word and forms a conjunction, and the word not expresses negation.

It will snow tomorrow, but it will not be cold.

The word but forms a conjunction, and the word not expresses negation.

It is cold today, but tomorrow it will be warm.

The word but forms a conjunction.

It is not cold today.

The word not expresses negation.

Which of the following English sentences use or with an inclusive meaning?

To enjoy winter, you have to know how to ski or how to skate. You cannot go on the ride if you are under 4 feet tall or if you weigh over 300 pounds.

Consider the propositions p and q, where p is "We will name our baby Mary" and q is "We will name our baby Philip." What is p XOR q?

We will name our baby Mary or Philip, but not both.

The sentence "Zaid does not have a newborn baby" is the ___________ of the statement "Zaid has a newborn baby."

negation