Problem 1. Formulate the negation of each of the statements below in a meaningfu

Question

Problem 1. Formulate the negation of each of the statements below in a meaningful way. Note: just writing "It is not the case that..." before each statement will not receive credit, as that does not help the reader understand the meaning of the negation. (a) Every integer has an additive inverse. (b) Some matrix has infinitely many columns (c) No one loves everybody. (d) Some differentiable functions are continuous. (e) Every odd number is prime. (f) For every set A, there exists a set B such that Ag B.

Explanation / Answer

a. Not all the integers have an additive inverse.

b. None of the matrix has infinitey many columns.

c. Some one Loves everybody.

d. None of the differentiable function is continuous.

e. Not all the odd numbers are prime.

f. For any set A, there exist a set B such that AB

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