De Morgan’s Laws: The negation of the “andand set and the “or set is
The core idea: The negation of a proposition is equivalent to negating each of its internalsub-propositions and changing the logical connectors
(“and” becomes “or”; “or” becomes “and”) The negation of the “and set”①: It is false that he is both tall and handsome= negation that he is both tall and handsome= negation of him being tall and handsome
= ¬(he is tall and handsome) = ¬(he is tall) or¬(he is handsome) = he is not tall, or not handsome
This answer has three meanings:① He is not tall but handsome ② He is tall but not handsome ③ He is neither tall nor handsome) (In most public examination questions, the answers are options ① and ②, with a mnemonic symbol being: choose the negation of the proposition)
Text Memory: The negation of both things being true is at least one thing being false (the false thing ≥1)
It can also be understood this way: The “and set” indicates that both must be satisfied for the event to occur. To refute this, it is sufficient to present at least one counterexample to negate the and set. This statement says he is both tall and handsome, to refute it: he is tall, but not handsome (he is not tall, but still handsome) (You say he is both tall and handsome, but clearly he is neither tall nor handsome)
The essence is to lower the standard, without needing to completely overturn, as long as one flaw is found, the entire “and” set statement can be negated.
The negation of the “or set”②: It is false that he will either take the civil service exam or the graduate school entrance exam= negation that he will either take the civil service exam or the graduate school entrance exam= negation that he will take the civil service exam or take the graduate school entrance exam
= ¬(he will either take the civil service exam or the graduate school entrance exam) = ¬(he will take the civil service exam) and ¬(he will take the graduate school entrance exam) = he will not take the civil service exam and he will not take the graduate school entrance exam
Text Memory: To negate the sentence of the “or set”, you must prove: neither of the two events can occur.
De Morgan’s Laws: The negation of “both” = at least one is not
The negation of “at least one”/ or= none
(2015 Guangdong)01. To swim in the deep water area of the swimming pool, two conditions must be met: one is to wear a swimming cap, and the other is to hold a deep water swimming certificate. Xiao Wang wore a swimming cap to swim in the deep water area, but was stopped by the staff..
Based on the above conditions, the following conditions must be true:
A.Xiao Wang cannot swim, swimming in the deep water area is relatively dangerous
B.Xiao Wang is a child and is not suitable for swimming in the deep water area
C.Xiao Wang does not have a deep water swimming certificate
D.Xiao Wang arrived at the swimming pool when the deep water area was already closed
Analysis: The first step is to see what the question is asking? It may examine knowledge related to negating propositions
The second step is to look at the question stem and conclude: Swimming in the deep water area= (wearing a swimming cap and having a deep water swimming certificate), this is an and set, both must be satisfied for it to be valid.
The third step: Now the question states:Xiao Wang wore a swimming cap to swim in the deep water area, but was stopped by the staff. This means both conditions of the and set (wearing a swimming cap and having a deep water swimming certificate) are satisfied, but Xiao Wang has not met at least one of them, which is why he was stopped by the staff, examining De Morgan’s Law, the negation of the and set.
The fourth step: Based on the above conditions, the following conditions must be true (meaning how to conclude that he was stopped by the staff), according to the third step, the negation of the and set, presenting one counterexample is sufficient. The question states that Xiao Wang wore a swimming cap, so the remaining condition is that he does not have a deep water swimming certificate, thus the answer isC.