Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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please answer Q5 only, thanks.

Q4. Simplify the following sentences in predicate logic so that all the negation symbols are
directly in front of a predicate. (For example, Vr (-0(1)) (-E(r))) is simplified,
because the negation symbols are directly in front of the predicates O and E. However,
Vr -(P(x) V E(x)) is not simplified.)
(i) -(3r (P(x) V (E(x) → S(x))))
(ii) -(Vz (E(r) A (P(x) →¬(3y G(x, y)))
Q5. Write a sentence in predicate logic (using the same predicates as above) which is true when
the domain is the class of positive integers (1, 2, 3, ...), but is false when the domain is the
class of all integers (...,-2, -1,0, 1, 2, ...). (You do not need to explain your answer.)
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Transcribed Image Text:Q4. Simplify the following sentences in predicate logic so that all the negation symbols are directly in front of a predicate. (For example, Vr (-0(1)) (-E(r))) is simplified, because the negation symbols are directly in front of the predicates O and E. However, Vr -(P(x) V E(x)) is not simplified.) (i) -(3r (P(x) V (E(x) → S(x)))) (ii) -(Vz (E(r) A (P(x) →¬(3y G(x, y))) Q5. Write a sentence in predicate logic (using the same predicates as above) which is true when the domain is the class of positive integers (1, 2, 3, ...), but is false when the domain is the class of all integers (...,-2, -1,0, 1, 2, ...). (You do not need to explain your answer.)
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