Discrete mathematical problems. Symbolization of propositions.

1, (1)P: I'll eat after I finish my homework. Q: It won't rain. R: We'll go to the ball game.

p∧Q-& gt； rare

(2)P: The weather is fine, Q: Here comes Lao Wang. p->； √Q

2，P→(Q→R) →^P∨(^Q∨R)→^P∨^Q∨R

Q→(P→R) →^Q∨(^P∨R)→^Q∨^P∨R

3. Find the principal disjunctive normal form of the formula: construct the truth table; Find by equivalent formula

4. (1)P(x): real number, Q(x): rational number (x exists) (p (x) → q (x))

(2)P(x): people, Q(x): making mistakes; ((X exists) (p (x) ∧ q (x)))

The "existence" symbol can't be typed, I hope everyone understands.