程序代写代做代考 Predicate Logic Some Exercises in Semantics

Predicate Logic Some Exercises in Semantics

Predicate Logic
Some Exercises in Semantics

With my thanks to everyone who has
taught logic in the Department

Assume the Universe of
integers  1

For each of the following decide if it is true or
false.

1. X (X is the product of two odd integers)

X, Y, Z (X=Y*Z  odd(Y)  odd(Z))

2. X (X is the product of two odd integers)

X Y, Z (X=Y*Z  odd(Y)  odd(Z))

3. Y X (X is an even factor of Y)

Y X, Z (Y=X*Z  even(X))

4. X Y (Y>X)

5. X Y (X*Y  X)

6. Y X (Y ≤ X)

7. Y X (X ≤ Y)

8. X (Y(X= Y2)  even(X))

9. X (Y ¬(X= Y2)  odd(X))

10. X (¬Y (X divides Y)  ¬(X=1) )

Answers

1. True. Take 15=3*5.

2. False. Take 20.

3. False. Take 15.

4. True. For every X take X+1.

5. True.

6. True. Y=1.

7. False.

8. False. Take X= 25.

25=52, but 25 is not even.

9. False. Take 24.

10.

X (¬Y (X divides Y)  ¬(X=1) ) 

X (X=1  Y (X divides Y) )

True.