LAP Logic Training Platform

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(1) Define by intension (by description or comprehension) the following sets defined by extension (or by enumeration):

1. [Exercise 1]

P={Huelva, Seville, Cordoba, Jaen, Cadiz, Malaga, Granada, Almeria}

Solution:

P= {x/ x is a province of Andalusia}

2. [Exercise 2]

P={ Antioquia, Bolivar, Boyaca, Caldas, Cauca, Choco, Cundinamarca, Huila, La Guajira, Meta, Narino, Norte de Santander, Santander, Sucre, Tolima, Valle del Cauca }

3. [Exercise 3]

P={1,2,3,4,5,6,7,8,9...}

Solution:

P={x/x is N (natural number)}

4. [Exercise 4]

P={...-3, -2, -1, 0, 1, 2, 3...}

5. [Exercise 5]

P={Set theory, Model theory, Proof theory, Computability theory... }

Solution:

P={x/x is a branch of mathematical logic}

6. [Exercise 6]

P={ <Julio Iglesias de la Cueva, Enrique Iglesias>, <Julio Iglesias de la Cueva, Julio Jose Iglesias>}

Solution:

P={<x,y>∈ CxC/ y is a child of singer Julio Iglesias} Where C, C={x/x is a singer}

7. [Exercise 7]

P={5, 10, 15, 20...}

Solution:

P={x/x is a multiple of 5}

8. [Exercise 8]

P= {...<1,-1>, <2, -2> <3, -3>, <4, -4>, <5, -5>...}

9. [Exercise 9]

P={<Luis Gutierrez Alvarez, 76849912A>, <Adrian Gomez Lerin, 48593254Z>, <Antonio Banderas Rodillo, 65749934H}

Solution:

P= {<x,y> ∈ HxD/ x has ID number y }

10. [Exercise 10]

P={<1,1>, <2,4>, <3, 9>, <4,16>, <5,25>...}

(2) Define by extension the following sets defined by intension:

11. [Exercise 11]

P={x∈ H/ x is a member of the Jackson Five}

Solution:

P={Michael Jackson, Jackie Jackson, Tito Jackson, Jermaine Jackson, Randy Jackson}

12. [Exercise 12]

P={x/x is a member of the Beatles}

13. [Exercise 13]

P= {x/ x² - 4=0}

Solution:

P={2}

14. [Exercise 14]

P={x/ x² - 48x + 578 = 0}

15. [Exercise 15]

P={x / x is one of the Harry Potter books}

Solution:

P={Harry Potter and the Philosopher's Stone, Harry Potter and the Chamber of Secrets, Harry Potter and the Prisoner of Azkaban, Harry Potter and the Goblet of Fire, Harry Potter and the Order of the Phoenix, Harry Potter and the Half-Blood Prince, Harry Potter and the Deathly Hallows...}

16. [Exercise 16]

P={x/x is a biotype}

17. [Exercise 17]

P={<x,y> ∈ N x N/ y= x+1}

Solution:

P={<1,2>, <2,3>, <3,4>, <4,5>...}

18. [Exercise 18]

P={<x,y> ∈ NxN/ x+y=170}

19. [Exercise 19]

P={<x,y> ∈ SxA/ y is the ASCII code of x} Where S is a computer symbol and A is an ASCII number.

Solution:

P={<NULL,00>, <SOH, 01>, <STX, 02>, <ETX, 03>, <EOT, 04>...}

20. [Exercise 20]

P={<x,y> ∈ NxR/ x is the number corresponding to y} Where N is natural numbers and R is numbers in the Roman numeral system.