Question

please let words clear, thanks

7. Recall that the notation alb is read as "a divides b" and means that there is some integer x such that b ax. Now consider the following sentence: a e a) Write the negation of the sentence above in symbols, simplifying whenever b) The ORIGINAL sentence above is false. Provide a counterexample that demonstrates this and explain why it is a counterexample. Hint: a counterexample for this statement would be a proof of its negation

Answer 1

"(Forall a elementof z) (Forall b elementof z) (14/a rightarrow (14/a 14/b)) To find negation as sentence, first we wise sec negative Forall a is exist a (Thus existence a) negative as ""a rightarrow b"" is ""a rightarrow ~b"" (a implies negative of B) negative of (A Intersection B) is (~A Intersection ~B) so negation as sentence 1 is (Forall a elementof z) (Forall b elementof z) (14/a rightarrow (14 times a Intersection 14 times b)) (x does not divide) i.e. such a, b elementof z for which 14/a implies 14 times a (is does not divide a) and 14 times b Counter example is a = 12, b = 15 (any number that is not divisible by 14) \r\n i.e. exist a, b elementof Z for which 14/12 or 14/15 fails but in the negation satisfy's this i.e. 14 times 12 and 14 times 15"