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.