Question 1 1
P (x): x is a student.
Q (x): The main task of X is learning.
x(P(x)→Q(x))
12 questions
If it is 2 pm, we will go to the auditorium to watch movies or go to the classroom to read books.
Please understand it this way:
R: It's two o'clock in the afternoon.
P: Let's go to the auditorium to see a movie.
Q: Let's go to the classroom and read.
r →( P∞Q)
13 questions
Error, you can give a counterexample: A: {0} B: {0, {0}} all meet the conditions.
Of course, you can also give a counterexample like this: B = A ∨{ A} both can be satisfied.
14 questions
Correct, in fact, you can draw a composition with the same composition (just connect the three vertices of a triangle with the center of the circle)
15 questions
( 1)R = { & lt； a，a & gt，& ltb，b & gt，& ltc，c & gt，& ltd，d & gt，& lta，b & gt，& lta，c & gt，& ltb，d & gt，& ltc，d & gt}
(2) Similar to Haas diagram, draw a closed ring (with arrows) at the nodes, and add arrows at the endpoints of line segments in the diagram.
(3) the largest element of b does not exist, the smallest element is a, and the upper bound is d.
16 questions
leave out
17 questions
P→(Q∧R)
P∨(Q∧R) becomes conjunctive disjunction.
(? P∨Q)∧(？ P∨R) distribution law
(? P∨Q∨(？ R∧R))∧(？ P∨(？ Q∧Q)∞R) supplement
((? P∨Q∨？ R)∧(？ P∨Q∨R))∧(？ P∨(？ Q∧Q)∨R) distribution law 2
(? P∨Q∨？ R)∧(？ P∨Q∨R)∧(？ P∨(？ Q∧Q)∨R) associative law
(? P∨Q∨？ R)∧(？ P∨Q∨R)∧((？ P∨？ Q∨R)∧(？ P∨Q∨R)) distribution law 2
(? P∨Q∨？ R)∧(？ P∨Q∨R)∧(？ P∨？ Q∨R)∧(？ P∨Q∨R) associative law
(? P∨Q∨？ R)∧(？ P∨？ Q∨R)∧(？ P∨Q∨R) idempotent law
Get the master conjunctive normal form, and then check the missing largest item.
m？ ∧M？ ∧M∏(4，5，6)
∏(0, 1,2,3,7)? ∑(0, 1,2,3,7)? m？ ∨m？ ∨m？ ∨m？ ∨m？
(P∨Q∨R)∨？ (P∨Q∨？ R)∨？ (P∨？ Q∨R)∨？ (P∨？ Q∨？ R)∨？ (? P∨？ Q∨？ De Morgan's law
(? P∧？ Q∧？ r)∩(？ P∧？ Q∧R)∨(？ P∧Q∧？ r)∩(？ P∧Q∧R)∨(P∧Q∧R) De Morgan's Law
Get the principal disjunctive normal form
18 questions
A∩(B-C)
=A∩(B∩？ c)
=A∩B∩？ C
=A∩B∩(？ a∨？ C) absorption rate
=(A∩B)∩(？ a∨？ C) binding rate
=(A∩B)∩？ (A∩C) De Morgan's Law
=(A∩B)-(A∩C)