1. (a) Express the following sentence in a formal language:
If every player beats some opponent in every tournament that features some champion from every country holding some title, then some player beats every opponent in some tournament that features every champion from some country holding every title.
(b) Draw a formula tree for the preceding sentence.

2. Draw a formula tree for the sentence that expresses Goldbach's Conjecture. (See one of the handouts from August 26 for the statement of Goldbach's Conjecture.)

3. Draw a formula tree for the sentence that expresses that $f$ is a continuous function. (See one of the handouts from August 26 for the formal statement expressing that $f$ is continuous.)

We will work on Problem 1 in class. You should submit Problems 2 and 3 by the due date.

1. (a) Express the following sentence in a formal language:
If every player beats some opponent in every tournament that features some champion from every country holding some title, then some player beats every opponent in some tournament that features every champion from some country holding every title.
(b) Draw a formula tree for the preceding sentence.

2. Draw a formula tree for the sentence that expresses Goldbach's Conjecture. (See one of the handouts from August 26 for the statement of Goldbach's Conjecture.)

3. Draw a formula tree for the sentence that expresses that $f$ is a continuous function. (See one of the handouts from August 26 for the formal statement expressing that $f$ is continuous.)

We will work on Problem 1 in class. You should submit Problems 2 and 3 by the due date.

HW1 solutions.pdf
HW1 solutions.tex

1. Exercise 10 of Section 1.5.

2. Exercise 2 of Section 1.5.

2. Exercise 5 of Section 1.5.

We will work on Problem 1 in class. You should submit Problems 2 and 3 by the due date.