(quantifiers.)
(a) without using any words of negation (i. e. without using the words not, no, nor, nei-
ther,. . ), write down a sentence that describes the negation of the following:
"in every cookbook i own, if there are dessert recipes in that book, then every dessert
recipe will contain an odd number of eggs and at least one dessert recipe will be
dairy-free."
(b) fermat's last theorem is the following claim:
"if n is an integer that is greater than or equal to 3, then there are no integers x, y, z
such that the equation x^n + y^n = z^n has a solution."
write this statement using quantifiers where possible. then write its negation.
(c) take an arbitrary set s, containing only integers that are greater than or equal to 2.
consider the following two propositions which s may or may not satisfy:
a: there is an integer d > = 2 such that for any n ? s, we have that d divides n.
b: for any n ? s, there is an integer d > = 2 such that d divides n.
i. write both of these statements using quantifiers wherever possible.
ii. is there any set s such that a is false? either create such a set, or explain why none
exists.
iii. is there any set s such that b is false? either create such a set, or explain why none
exists.
iv. are a and b equivalent propositions?
you!