Current location - Training Enrollment Network - Mathematics courses - Steps of discrete mathematics 13(6) and the explanation of each step.
Steps of discrete mathematics 13(6) and the explanation of each step.
Answer to question (6):

(? R∨(Q→P))→(P→(Q∨R))

(? R∨(Q→P))∨(P→(Q∨R)) becomes a conjunctive disjunction.

(? R∨(? Q∨P))∨(? P∨(Q∨R)) becomes conjunctive disjunction.

(? R∨(P∨? Q))∨(? Ordering of P∨(Q∨R)) permutation law

(R∧? (P∨? Q))∨(? P∨(Q∨R)) De Morgan's Law

(R∧(? P∧Q))∨(? P∨(Q∨R)) De Morgan's Law

(R∧? P∧Q)∨? P∨(Q∨R) associative law

(R∧? P∧Q)∨? P∨Q∨R associative law

(? P∧Q∧R)∨? Ordering of P∨Q∨R commutative laws

P∨Q∨R conjunctive disjunctive absorption rate

Get the master conjunctive normal form, and then check the missing largest item.

M∏(4)

∏(0, 1,2,3,5,6,7)? ∑(0, 1,2,3,5,6,7)? m? ∨m? ∨m? ∨m? ∨m? ∨m? ∨m?

(P∨Q∨R)∨? (P∨Q∨? R)∨? (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)∨(P∧Q∧? R)∨(P∧Q∧R) De Morgan's Law

Get the principal disjunctive normal form