Acid rain causes both the pH of water and the level of alumi…
Acid rain causes both the pH of water and the level of aluminum in water to decrease.
Acid rain causes both the pH of water and the level of alumi…
Questions
Acid rаin cаuses bоth the pH оf wаter and the level оf aluminum in water to decrease.
(10 pts) Shоw thаt the fоllоwing compound proposition is а tаutology. [ p ∧ ( p → q)] → q Let E denote the set of even integers and O denote the set of odd integers. Let Z denote the set of all integers. Determine each of these sets. (10 pts) E U O E ∩ O Z - E Z - O Let f and g be functions from {1,2,3,4} to {a , b, c ,d} and from {a , b, c ,d} to {1,2,3,4} respectively, with f(1) = d, f(2) = c, f(3) = a, and f(4) = b, and g(a) = 2, g(b) = 1, g(c) =3 and g(d) = 2. (10 pts) Are f and g one-to-one Are f and g onto (10 pts) Find the gcd of 123 and 277 using Euclidean Algorithm. How many divisions does it take to find the gcd? (10 pts) Find the solution to the following linear congruence 2x ≡ 6 (mod 17). Use mathematical induction to prove that 2 divides n2 + n whenever n is a positive integer.(10pts) In how many ways can a set of five letters be selected from the English alphabet?(10pts) 8. How many ways are there to choose 4 items from 12 distinct items when (10 pts) The items in the choice are ordered and repetition is not allowed? The items in the choice are ordered and repetition is allowed? The items in the choice are unordered and repetition is not allowed? The items in the choice are unordered and repetition is allowed? (10 pts) A fair coin is tossed twice such that E: event of having both head and tail, and F: event of having atmost one tail. Find the conditional probability of E given F. 10. Suppose that there are nine students in a discrete mathematics class at a small college. a) Show that the class must have at least five male students or at least five female students. b) Show that the class must have at least three male students or at least seven female students.