Question

# Discrete Mathematics (a) Let P(x) be the predicate “−10 < x < 10” with domain Z+...

Discrete Mathematics

(a) Let P(x) be the predicate “−10 < x < 10” with domain Z+ (the set of all positive integers). Find the truth set of P(x).
(b) Rewrite the statement Everybody trusts somebody in formal language using the quantiﬁers ∀ and ∃, the variables x and y, and a predicate P(x,y) that you must deﬁne.

(c) Write the negation of the statement in (b) both formally and informally.

#### Homework Answers

Answer #1

Sol:

a).

=  .

So x < 10 and   x = 1, x=2 ,...... x = 9.

So Trusth set is   s =

b).

P(x,y) : x trusth y.

c).

Negation : .

Informally, there is a person , who does not trust anybody.

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