On Discrete Mathematics p - > (Q - > P) The original question is like this Non p - > (P - > q) P - > (Q - > P) How is it proved?

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• 1. How to deduce the discrete mathematics P → (P → q) P → q? And what is the value of P ∨ P, P ∧ p
• 2. Draw a simple graph with four vertices Be sure to draw a picture
• 3. The problem of set transitivity in discrete mathematics Let a = {a, B, C}, then the above relation R={,,,} S = {} is transitive Why are R and s transitive? Can r be understood as not meeting all the delivery possibilities?
• 4. Transitivity R1 = {(a, b), (B, c), (a, c)}, R1 is transitive, and R2 = {(a, b), (B, c), (a, c), (C, a)} is this transitive? That is, there can be no redundant ordered pairs that can be reused?
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• 7. In discrete mathematics, the definition of binary relation on set (a, B, c) and why it is transitive relation is related to their relation It doesn't match, it doesn't match the symmetry
• 8. How is the binary relation calculated? R1={(a,b),(c,d)},R2={(b,c),(d,e)} So R1 * R2 = {(a, c)}, R2 * R1 = {(B, d)} What do I think, R1 * R2 = {(a, c), (C, e)}, Because (a, b) (B, c) can get (a, c) (C, d) (D, e) can get (C, e)
• 9. Discrete mathematics problem, let R be a binary relation on a, define s = {(a, b) | &; C ∈ a, (a, c) ∈ R, (C, b) ∈ r}, prove Let R be a binary relation on a, define s = {(a, b) | &; C ∈ a, (a, c) ∈ R, (C, b) ∈ r}, prove that if R is an equivalence relation on a, then s is also an equivalence relation, and S = R It's OK to connect~
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• 11. What does P mean if and only if Q in discrete mathematics
• 12. On the problem of graph It is known that: "in a graph of order n, if there is a path from vertex u to vertex v (U is not equal to V), then there must be a primary path from u to V, and the length of the path is less than n-1." and "in a graph of order n, the length of any primary circuit is not greater than n." my question is: the primary path includes the primary circuit, so why is the length of any primary circuit not greater than N, rather than n-1 in a graph of order n?
• 13. Discrete mathematics problem map urgent! What is the difference between the complement of a subgraph relative to the original graph and the complement of a complete graph?
• 14. A certain element of hastu is not comparable with several elements of different layers. Which layer is it drawn on
• 15. The partial order relation on the set a = {2,3,6,12,24,36} is an integral division relation, which is to draw a Haas diagram. How to find Cova? Explain the specific lecture in detail
• 16. How to judge the maximum, minimum, maximum and minimum elements according to hastur's intuitionistic judgment, that is, a = {1,2 ·· 9}, R is the partial ordered set of integral division of A, Draw its hastur, and judge its maximum, minimum, maximum and minimum elements
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• 19. Let a be an sxn matrix and B be an mxn matrix composed of the first m rows of A. It is proved that if the rank of the row vector group of a is r, then R (b) > = R + m-s
• 20. It is proved that the mxn matrix A with rank r (r > 0) can be decomposed into the sum of R mxn matrices with rank 1 Is m x n matrix Detailed process