Negate the following statement. Also decide whether the given statement or its negation is true:For all x , y ∈ R such that x y ≠ 0 we have that 1 x + 1 y = 1 x + y

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Negate the following statement. Also decide whether the given statement or its negation is true:For all   x  ,  y  ∈  R such that   x  y  ≠  0 we have that      1    x    +      1    y    =      1          x      +      y

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Step 1Given statement is: For all   x  ,  y  ∈  R such that   x  y  ≠  0 we have that      1    x    +      1    y    =      1          x      +      y      Suppose   x  =  2  ∈  R     and     y  =  3  ∈  RNow,       1    x    +      1    y    =      1    2    +      1    3    =            3      +      2        6    =      5    6  And,       1          x      +      y        =      1          2      +      3        =      1    5  Since       5    6    ≠      1    5  , then       1    x    +      1    y    ≠      1          x      +      y      Step 2Therefore, the given statement is not true.Hence, the negation of the given statement is true.

Negate the following statement. Also decide whether the given statement or its negation is true: For al x, y in R such that xy ne 0 we have that 1/x+1/y=1/(x+y)

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