Please help me with these 2 problems
a) Express the statement "Every negative number has another negative number greater than it" using quantifiers.
b) Express the negation with no negation symbols in front of quantifiers, and then state the negation in words.
c) Is the statement true for the integers? For the rationals?
so I for part a) i did ∀x∃y[( x< 0 Y <0) --> x < y ) , the statement is false because if x = -1 , there is no negative number greater than -1
i'm not sure how to do the negation , but i'm sure that the negation statement is true for the integers, not sure for the rationals.
2) Find the general solution of the recurrence relation a1 = 1 , a2 = 2, an = 7an-1 - 10 an-2 + 3n + 8
I got an = (-2) (2)n + (17/10) (5)n -(9/2) 3n +2, but i think i got the coefficient (-2) and (17/10) are wrong.