Let x-,2,3, 4, 5, 6, 7, 8 and let t be a topology on x. let a- , 3, 5,7 (a). find all closed sets in t. (b). find neighborhoods of 1 and 7 (c). find int(a) (d). find a. (e). find aa(boundary of a). (f). is t hausdorf?

(a) (8%) compute the probability of an even integer among the 100 integers 1! , 2! , 3! , until 100! (here n! is n factorial or n*(n-1)*(n-2) *… 1) (b) (16%) compute the probability of an even integer among the 100 integers: 1, 1+2, 1+2+3, 1+2+3+4, …., 1+2+3+… + 99, and 1+2+3+… + 100

Which ordered pair (c,d) is a solution to the given system of linear equations- c+2d=13 -9c-4d=-15

What properties allow transformation to be used as a problem solving tool