But does your example fit the relation? Don't the variables have to be integers?
Going by your definition, if I do find a few cases that fit the relation and a few that don't, does that still mean the relation is an equivalence relation? Therefore, if let's say all variables are the same, ie...
1. Homework Statement
Let X be Z*Z, i.e. X is the set of all ordered pairs of the form (x; y) with (x, y) are integers.
Define the relation R on X as follows:
(x1^2, x2^2)R(y1^2, y2^2) = (x1^2 + x2^2) = (y1^2 + y2^2)
2. Homework Equations
By definition, an equivalence relation bears...
1. Homework Statement http:
What is the largest number which is the order of an element of S_8? Write down
an element of that order in disjoint cycle notation.
2. Homework Equations
3. The Attempt at a Solution
To start with, I don't understand the wording of the question. When...
oh right right!
in other words,
f(1) = 1
f(2) = 2
f(3) = 2
functions f(2) and f(3) would have been injections had a and b in the following f(a) = f(b)were equal which is not the case here? Surjections have have the property that for every y in the codomain there is an x in the domain such...
1. Homework Statement
List all the functions from {1,2,3} to {1,2} representing each function as an arrow
diagram. Which of these functions are (a) injective, (b) surjective, (c) bijective? For
each surjective function write down a right inverse.
2. Homework Equations
3. The Attempt...
hmm I see, I never did that before, I simply went on with the integrating whenever it was 1/2-1/2cos2t for example....and I always obtained the right answer, weird! But thank you!
Following your reasoning, 1/2*sin(2t) becomes 2x*sqrt(1-x²). The two cancels out when I plug it back into 1/2*sin(2t), and this can't be since the answer is 1/2*x*sqrt(1-x²)??!
1. Homework Statement
After integrating x²/(sqrt1-x²) using the triangle method and thereby substituting sin¤ for x, I ended up with the result 1/2¤-1/2sin2¤+c. For my answer toge complete, I must have the ¤ in x format. I managed to convert the 1/2¤, which is simply 1/2arcsinx but I couldn't...
1. Homework Statement
After integrating x²/(sqrt1-x²) using the triangle method and thereby substituting sin¤ for x, I ended up with the result 1/2¤-1/2sin2¤+c. For my answer toge complete, I must have the ¤ in x format. I managed to convert the 1/2¤, which is simply 1/2arcsinx but I couldn't...
1. Homework Statement
In the previous question, we're asked to determine the average flow rate from 00:00 on 28 October to 00:00 on 2 November, which I did by finding the slope connecting these two points. The slope is -1/6 and so the average rate is -1/6 cfs/hours. The question that follows...