1. Show by specific counterexample that the following statements are false.
(a) " for all ."
(b) "The square of a real number is greater than or equal to the original number."
(c) "If m and n are integers and 6 divides , then either 6 divides m or 6 divides n."
(d) "The derivative of a product of two functions is equal to the product of the derivatives of the two functions."
(a) If , , while . Therefore, the result is false.
(b) If , then , but is not greater than or equal to . Therefore, the result is false.
(c) If and , then 6 divides , but 6 does not divide either or . Therefore, the result is false.
(d) Let and . Then
Therefore, the result is false.
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