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Prove that for all sets A and B:
A⊆B ⇐⇒ A∪B=B.
A⊆B ⇐⇒ A∪B=B.
In a large statistics class, suppose 50%of the students are studying bachelor of science, 20% are studying forensic science, 10% studying environmental sciences and remaining 20% are From variety of other degrees.
Explain how you could assign random numbers to represent the degrees studied using table of random digits
Explain how you could assign random numbers to represent the degrees studied using table of random digits
How many ways can you assign 4 caretakers each of which look after 2 lighthouses for a year (for a total of 8 lighthouses), and then assign each two lighthouses in the next year so that none of them tend the same two lighthouses both years?
How many ways can you assign 4 caretakers each of which look after 2 lighthouses for a year (for a total of 8 lighthouses), and then assign each two lighthouses in the next year so that none of them tend the same two lighthouses both years?
Find a generating function in closed form for the sequence:
{1,2,3,4,1,2,3,4,1,2,3,4,...}
{1,2,3,4,1,2,3,4,1,2,3,4,...}
How many permutations of the 26 letters of our alphabet do not contain any of the three strings "US", "AIM", and "DONKEY"?
New domain of the function f given by f x is equal to under root 2 - X upon X is zero one is it true or false give reason
Find the indicated limit, if it exists.
limit of f of x as x approaches negative 1 where f of x equals 4 minus x when x is less than negative 1, 5 when x equals negative 1, and x plus 6 when x is greater than negative 1
limit of f of x as x approaches negative 1 where f of x equals 4 minus x when x is less than negative 1, 5 when x equals negative 1, and x plus 6 when x is greater than negative 1
Let X be a non-empty set, and let R be an equivalence relation on X. Let C be the set of all equivalence classes of R. So C={A⊆X such that A=[x] for some x ∈ X}.
Now, define f : X → C by the rule f(x) = [x] for all x ∈ X.
Prove that if x ∈ X, then there is one and only one equivalence class which contains x.
Suppose X = {1, 2, 3, 4, 5} and that R is an equivalence relation for which 1 R 3, 2 R 4 but 1 R̸ 2,1 R̸ 5,and 2 R̸ 5.
Write down the equivalence classes of R and draw a diagram to represent the function f.
Now, define f : X → C by the rule f(x) = [x] for all x ∈ X.
Prove that if x ∈ X, then there is one and only one equivalence class which contains x.
Suppose X = {1, 2, 3, 4, 5} and that R is an equivalence relation for which 1 R 3, 2 R 4 but 1 R̸ 2,1 R̸ 5,and 2 R̸ 5.
Write down the equivalence classes of R and draw a diagram to represent the function f.
Find the indicated limit, if it exists.
limit of f of x as x approaches 0 where f of x equals 5 x minus 9 when x is less than 0 and the absolute value of the quantity 2 minus x when x is greater than or equal to 0
limit of f of x as x approaches 0 where f of x equals 5 x minus 9 when x is less than 0 and the absolute value of the quantity 2 minus x when x is greater than or equal to 0
