Theory of Automata

Quantifiers

Determine whether each of the following is true or false. by prime(k) we mean k is prime. By even(k) we mean k is divisible by 2.

1. z{4..5}.(z<5)

2. x{1..10}. x + 2 > 0

3. x{1..10}. x - 2 > 0

4. x{10..5}. x < 0

5. x{1..15}. y{1..15}. x < y

6. x{1..100}. x < 2x

7. kN.(k > 1 k > 0)

8. kN. (k = 4 k > 10 0 = 1)

9. kN. (prime(k) k > 1)

10. iN.jN. i < j

11. iN.jN. i < j

12. xR.yR. x < y

13. yR.xR. x < y

14. iN. (i > 0 kN. k > i)

15. kN.(prime(k) even(k))