( 1)? (q∧r) p rule

(2)? q∨？ r ( 1)

(3) Republican rules

(4)? Question (2)(3)

(5)p→q p rule

(6)? Article 4, paragraph 5

4. It is proved that if g is not connected, then K (G) = λ (G) = 0, so the above formula holds. If G is connected, 1) proves that λ(G)≤δ(G) If G is trivial, λ (G) = 0 ≤δ (G). If g is extraordinary, then each.

2) It is proved that k(G)≤λ(G) (a) is λ(G) = 1, that is, G is trimmed. Obviously, when K (g) = 1, the above formula holds. (b) Let λ(G)≥2, then a λ(G) can be deleted. 5). For each λ(G)- 1 edge, choose an endpoint different from U and V. If these endpoints are deleted, at least λ(G)- 1 edge must be deleted. If the graph generated in this way is disconnected, then k(G)≤λ(G)-65438+.

Five,

( 1)(? x)(P(x)→Q(x))∧(？ x)(R(x)→？ Q(x)) p rule

(2)(? x)(P(x)→Q(x))， 1

(3)(? x)(R(x)→？ Q(x)) ( 1)

(4)P(a)→Q(a) (2)

(5)? Q(a)→？ P(a) (4)

(6)R(a)→？ Question (a) (3)

(7)R(a)→？ P(a) (5)(6)

(8)(? x)(R(x)→？ P(x)) (7)