How to negate a disjunction

I am a little confused with Enumerator#reject in ruby. Consider the following code:

(1..10).select {|i| i % 3 == 0 || i % 5 == 0 } => [3, 5, 6, 9, 10]

Shouldn't the following line be equivalent?

(1..10).reject {|i| i % 3 != 0 || i % 5 != 0 } => []

If I just use one condition on the reject method, the result is as expected. but If I include the OR operator the res开发者_Python百科ult turns out to be empty. Could somebody clarify this for me.

(1..10).reject {|i| i % 3 != 0} => [3, 6, 9]

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You are making a basic logic mistake:

!(A || B) is equivalent to !A && !B and NOT equivalent to !A || !B.

So if you change the || in your second example to a &&, then your second example would give the same result as the first:

(1..10).reject {|i| i % 3 != 0 && i % 5 != 0 } # => [3, 5, 6, 9, 10]

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You have run into one of De Morgan's laws.

p And q = Not((Not p) Or   (Not q))
p Or   q = Not((Not p) And (Not q))

It was close, but you forgot to change the operator.

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In the second piece of code, you changed the equality, so you'll need to change the || to &&.

(1..10).reject {|i| i % 3 != 0 && i % 5 != 0 } => [3, 5, 6, 9, 10]