1) Prove that if A⊨tautB and C⊨tautD then A∨C⊨tautB∨D . 2) Show that the formulae A≡⊥ and ¬A are tautologically equivalent.

The weight of an object in a particular scale is 175.2 lbs. the measured weight may vary from the actual weight by at most 0.1 lbs. what is the range of actual weights of the object

Hector and alex traded video games. alex gave hector one fourth of his video games in exchange for 6 video games. then he sold 3 video games and gave 2 video games to his brother. alex ended up with 16 video games. how many video games did alex have when he started?

A. plot the data for the functions f(x) and g(x) on a grid and connect the points. x -2 -1 0 1 2 f(x) 1/9 1/3 1 3 9 x -2 -1 0 1 2 g(x) -4 -2 0 2 4 b. which function could be described as exponential and which as linear? explain. c. if the functions continue with the same pattern, will the function values ever be equal? if so, give estimates for the value of x that will make the function values equals. if not, explain why the function values will never be equal.