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Here is a nice way to think about the negation of statements that have or or and.
1. Or Statements: Fido is a member of set A or set B.
2. And Statements: Spot is a member of set A and of set B.
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In the game of Clue, there are 3 playing cards in an envelope. One card is a weapon, one is a room, and one is a person. All of the other cards are dealt to the players. If someone guesses that it was "Miss Scarlet with the wrench in the kitchen" and you have one or more of these cards, then you must show the person who guessed one of the cards.
Original Statement: "The 3 cards in the envelope are Miss Scarlet, the Wrench, and the Kitchen."
Negation of Statement: "One of the cards, either Miss Scarlet or the Wrench or the Kitchen is in my hand or another player's hand."
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• Continue to love, but cease to cherish.
• Continue to cherish, but cease to love.
• Cease loving and cherishing.
This is one of the things I like about mathematics and logic. For me, there is a comfort in being able to analyze something, write it down, and realize "I really do understand this particular concept."