Solutions to Exercises for Section 5.4, Part II
For Interpretation 2
6. 2 is odd.
8. 2 is neither odd nor prime.
9. Every natural number is both odd and even.
10. It’s not the case that 2 is even only if 3 is odd.
11. If every natural number is odd, then 2 is prime.
12. Some natural number is odd if it is prime.
14. Not all natural numbers are prime.
15. Some natural number is either prime or not.
16. If both 2 and 3 are odd, then every natural number is odd.
17. All odd natural numbers are prime.
18. 3 is greater than 2, and 2 is not greater than 3.
19. Some natural number is greater than 2.
20. No natural number is greater than all natural numbers.
22. No natural number than which another natural number is greater is greater than that other natural number.
23. Any prime natural number that is greater than 2 is odd.
Solutions to Exercises for Section 5.5
1. I2: True.
2. I2: False.
4. I2: True.
5. I2: True.
6. I2: True.
8. I2: False.
9. I2: True.
10 I2: False.
11. I2: False.
12. I2: True.
14. I2: True.
15. I2: True.
For the following solutions, the interpretation on the left is an interpretation under which the relevant statement is false, and the interpretation on the right is an interpretation under which the relevant statement is true.
16. D: people D: people
Ax: x is a person Ax: x is a person
r: Fido (the dog) r: Joe Biden
17. D: people D: people
Ax: x is a person Ax: x is a person
Bx: x is a dog Bx: x is a daughter
18. D: people D: people
Ax: x is a person Ax: x is a person
Bx: x is a dog Bx: x is male
r: Joe Biden r: Joe Biden
20. D: people D: people
Ax: x is an astronaut Ax: x is an astronaut
Bx: x is male Bx: x is a human being
21. D: people D: people
Mx: x is male Mx: x is male
Bx: x is a professional basketball player Bx: x is a professional basketball player
g: Joe Biden g: Sarah Palin
More to come!