Download Problems on predicates

Exercise on Predicates
1. Write the expressions for the following sentences:
1. Some books are interesting.
2. All books written by Dickens are interesting.
3. No test is difficult
2. Write in English the expressions:
1.  x (movie(x) and boring(x))
2.  x prime(x) → odd(x) V (x = 2)
 x ((number(x) and prime(x))  odd(x))
x ( y friend(x,y)  ~lonely(x))
3. For each of the following statements do the following
 write the statement in Predicate logic
 write the negation of the logical expression, so that the negations appear only
with predicates (i.e. no negation is outside a quantifier or an expression
involving logical connectives)
 translate the negated formula in English
3. 1. Horses do not fly.
expression:
negation:
translation:
3. 2. Some horses do not fly.
expression:
negation:
translation:
3.3. No rational numbers are integers.
expression:
negation:
translation:
3.4. Some students are programmers and poets.
expression:
negation:
translation:
3.5. All students are programmers or poets.
expression:
negation:
translation:
3.6. Only US citizens can be presidents or vice-presidents.
expression:
negation:
translation:
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3. 7. Pigs do not have wings.
expression:
negation:
translation:
3. 8. Some pigs do not have wings.
expression:
negation:
translation:
3.9. No irrational numbers are integers.
expression:
negation:
translation:
3.10. Some real numbers are rational and positive.
expression:
negation:
translation:
3.11. All integers are negative or zero.
expression:
negation:
translation:
3.12. Only integers can be even or odd.
expression:
negation:
translation:
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4. Consider the expression:
 n (integer(n)  even_square(n)  even(n))
Which of the following sentences are equivalent to the above expression:
a.
b.
c.
d.
e.
All integers have even squares and are even.
Given any integer whose square is even, that integer is itself even.
There are some integers whose square is even.
Any integer with an even square is even.
All even integers have even squares.
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