Question

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.

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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