Consider the problem of reasoning about the identity of a set from the size of its intersections with other sets. you are given a finite set u of size n, and a collection a1, . . , am of subsets of u. you are also given numbers c1, . . , cm. the question is:
1. does there exist a set x ⊂ u so that for each i = 1, 2, . . , m, the cardinality of x ∩ ai is equal to ci?
we will call this an instance of the intersection inference problem, with input u, {ai}, and {ci}.
2. prove that intersection inference is np-complete.

If x + 10 = 70, what is x? a. 40 b. 50 c. 60 d. 70 e. 80

Cone w has a radius of 8 cm and a height of 5 cm. square pyramid x has the same base area and height as cone w. paul and manuel disagree on how the volumes of cone w and square pyramid x are related. examine their arguments. which statement explains whose argument is correct and why? paul manuel the volume of square pyramid x is equal to the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is three times the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is (area of base)(h) = (200.96)(5) = 1,004.8 cm3. paul's argument is correct; manuel used the incorrect formula to find the volume of square pyramid x. paul's argument is correct; manuel used the incorrect base area to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect formula to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect base area to find the volume of square pyramid x.

The value of the expression 16-^3/4 8 1/8 -6 6 1/40 1/64