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Unformatted text preview: ( x = y 2 ): (False) Suppose x = a satis±es the above statement. This means that a = y 2 for all real values of y . This is impossible since y would then be equal at most 2 real values ( ± √ a ). 2. ∃ x ∀ y ( xy = 0): (True) At x = 0, xy = 0 for all real values of y . 3. ∀ x n =0 ∃ y xy = 1: (True) If we pick an arbitrary value for x n = 0, say a , then there exists a value for y that satis±es the given statement, y = 1 a . 4. ∃ x ∃ y ( x + y n = y + x ): (False) The addition of real numbers is always commutative operation. 2...
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 Fall '08
 W.Szpankowski
 Logic, Addition, Logical connective, real values

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