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Question: Suppose that f is a function from the set A to the set B. Prove that
a) if f is one-to-one, then Sf is a one-to-one function from P(A) to P(B).
b) if f is onto function, then Sf is an onto function from P(A) to P(B).
c) if f is onto function, then Sf -1 is a one-to-one function from P(B) to P(A).
d) if f is one-to-one, then Sƒ -1 is an onto function from P(B) to P(A).
e) if f is a one-to-one correspondence, then Sƒ is a oneto-one correspondence from P(A) to P(B) and Sƒ -1 is a one-to-one correspondence from P(B) to P(A).
With the resulting matrix from part (a), add column 1 to column 2, then add this new column 2 to column 3, and so on, and explain why this does not change the determinant.
the scale of a model car is 1 inch 2.5 feet. the length of the model car is 6 inches. the width of the model car is
if a spool has a dimater of 7 centimeters, how many revolutions of the spool would you need to wind up a kite string that is 30 meters long? Please show work.
Calculate the effective address time if average page fault service time of 20 millisec and a memory access time of 80ns. Let us assume the probability of a page fault 10%
the area of the rectangular slab of foam insulation in the illustration is 36 square and the weith is (2w+1)meters. find the dimension of the slab.
RETIREMENT FUNDS Five and a half years ago, Chris invested $10,000 in a retirement fund that grew at the rate of 10.82%/year compounded quarterly.
Explain why the roots of the equation p(x) divided by g(x)=0 are the same as the zeros of the function p(x) if these are different from the zeros of q(x).
Determine the optimal production plan, i.e. , how many cupboards to produce each day in order to minimize the total production cost.
1. let x represent the number of units produced and sold and let p represent the total profit. with aprofit of 100 per
The formula d = , where h equals the height, in feet, of the viewer's eyes, estimates the distance d, in miles, to the horizon from the viewer. Find the distance to the horizon for a person who eyes are 6 ft above the ground.
before 1918 approximately 60 of the wolves in the new mexico and arizona region were male and 40 were female. however
a random sample of 36 cats found the average weight to be 9.8 pounds with a standard deviation of 2.4 pounds.a.
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