(1) Please write the negations of the following statements, referring to Section 1.3 of\ the Hutchings notes if you need help. (BTW, no fair just writing "It is not the case\ that..." at the beginning . Really write down the negation, i.e., the statement that\ is true precisely when the original statement is false.) You needn't use symbols.\ English sentences are fine, as long as they mean what you mean them to mean.:\ (a) "All integers are even."\ (b) "There exists an integer that is even."\ (c) "There exists an

xinZ

such that there exists a

yinZ

with

x=2y

."\ (d) "For all

xinZ

, if there exists

yinZ

such that

x=2y+1

then there exists\

zinZ

such that

x^(2)=2z+1.