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How to Understand the Laws of de Morgan Boolean Expressions

I squinted, trying to understand this expression. I thought several times, but I can not understand the meaning.

  • ! (p || q) is equivalent to | p & &! q For this, I somehow can understand a little. My understanding: "Not (pq) = not p, not q", which is understandable [/ p>

  • ! (p & q) is equivalent to | p ||! q Secondly, they completely turned me over. Why My understanding is "Not (pq) = no p or no q". How to come and / or be equivalent to each other? as for the rule in the truth table between && and || is different.

The way I understand each expression, maybe I have the wrong method in understanding the expression. Could you tell me how to understand these expressions?

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Truth, , . :

!(P || Q) = !P && !Q 

_________________________________________________
   P   Q   P || Q   !(P||Q)   !P   !Q   !P && !Q
_________________________________________________
   1   1      1         0      0    0       0
   1   0      1         0      0    1       0
   0   1      1         0      1    0       0
   0   0      0         1      1    1       1
_________________________________________________

, ! (P || Q) , ! P & &! Q. , P Q. .

!(P && Q) = !P || !Q 

_________________________________________________
   P   Q   P && Q   !(P&&Q)   !P   !Q   !P && !Q
_________________________________________________
   1   1      1         0      0    0       0
   1   0      0         1      0    1       1
   0   1      0         1      1    0       1
   0   0      0         1      1    1       1
_________________________________________________
+5

Red Toyota.

p = " "

q = " - Toyota"

! (p & q) " Toyota"

, :

! p ||! q " , () Toyota", ?

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