Predicate logic in Discrete Mathematics All athletes admire some coaches (a (x, y)) and some college students don't admire athletes. Write the predicate expressions of the above two sentences. Carry in the free variables of the following formulas. ((Any Y) P (x, y) ^ (z) Q (x, z)) V (any x) r (x, y)

Predicate logic in Discrete Mathematics All athletes admire some coaches (a (x, y)) and some college students don't admire athletes. Write the predicate expressions of the above two sentences. Carry in the free variables of the following formulas. ((Any Y) P (x, y) ^ (z) Q (x, z)) V (any x) r (x, y)

Define predicate:
A (x, y): X admires y;
Variable individual field:
X: athletes;
Y: coach;
Z: college students;
1. (any x) (exists y) a (x, y);
2. (exist z) (arbitrary x) & # 172; a;
3. ((y) P (s, y) ∧ (z) Q (s, z)) ∨ (x) r (x, t));

Predicate logic problem
Help me to prove the formula or illustrate with examples, that is to bring things in life
V is arbitrary, e is existence.
The formula is
Vx(A(x)->B) E(x)A(x)->B
It can be deduced from each other, that is, equivalent.
See page 6 of discrete mathematics course of Peking University Edition for details

A good way to prove equivalence, especially in logic, is to use a theorem: the original proposition and the inverse proposition are equivalent
So you can directly reverse the original proposition, remember whether e is V, and whether V is e
Let me give you a specific example: on earth, V is a living organism, and its collective chemical composition contains carbon
Detection of chemical composition does not contain carbon group -- > e an inanimate

Discrete mathematical problems, predicate logic problems, solving, thank you!
First symbolize the following proposition, then deduce its conclusion. (8 points)
If a person is afraid of difficulties, he will not succeed. Everyone either succeeds or fails. Some people do not fail. Therefore, there are people who are not afraid of difficulties

F (x): X is afraid of difficulties, G (x): X will succeed, H (x): X will fail. Premise: ax (f (x) → g (x)), ax (g (x) ∨ H (x)), ex (∨ H (x)) conclusion: ex (∨ f (x)) proves: 1 ex (∨ H (x)) 2 h (c) 1ei3 ax (g (x) ∨ H (x)) 4

A problem of logic
To get tenure as a professor,it is sufficient to be world-famous.
Which push which?

A sufficient condition for world fame to be a tenure Professor