Use equivalences to show that the equations are equivalent ∀x p(x) ∧ ∃y q(y, x) → ∃y r(y) ≡ ∃z ¬p(z) ∨ ∀y ¬q(y, x) ∨ ∃w r(w)

Asequence {an} is defined recursively, with a1 = 1, a2 = 2 and, for n > 2, an = an-1 an-2 . find the term a241. a) 0 b) 1 c) 2 d) 1 2

Worth 100 points need the answers asap first row -x^2 2x^2 (x/2)^2 x^2 x is less than 2 x is greater than 2 x is less than or equal to 2 x is greater than or equal to 2 second row -5 -5/2 4 5 •2 is less than x& x is less than 4 •2 is less than or equal to x & x is less than or equal to 4 •2 is less than or equal to x& x is less than 4 •2 is less than x& x is less than or equal to 4

Xf(x) = 2x + 5 1 7 2 9 3 11 4 13 5 15 6 17 linear functions grow by equal differences over equal intervals. in the table above, what column could be added to prove this relationship?