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a) Let V = f1, 2, :::, 7g and define R on V by xRy iff x - y is a multiple of 3. You should know by now that R is an equivalence relation on V . Suppose that this is so. Explain the partition of V induced by R.
b) Let A = {1, 2, 3, 4} and define R on P(A) -{Ø} by xRy iff x ∩y ≠Ø. Is R an equivalence relation? Describe
Write down the equation of the line which passes through the points (2, -1, 3) and (1, 4, -3). Write all three forms of the equation of the line. Solution To do the above
Determine the function f ( x ) . f ′ ( x )= 4x 3 - 9 + 2 sin x + 7e x , f (0) = 15 Solution The first step is to integrate to fine out the most general pos
The next thing that we must acknowledge is that all of the properties for exponents . This includes the more general rational exponent that we haven't looked at yet. Now the pr
the base b of a triangle increases at the rate of 2cm per second, and height h decreases at the rate of 1/2 cm per second. Find rate of change of its area when the base and height
More Optimization Problems Example A window is being built in which the bottom is rectangle and the top is a semicircle. If there framing materials is 12 meters what have
solve the following simultaneous equations x+y=a+b ; a/x_b/y
Example of mathematical operations: Example: Solve the following equation: [2 .( 3 + 5) - 5 + 2] x 3 = ________ Solution: a. Perform operations with
26 + 34=
what is -6.4 as a fraction?
Q. Multiplying Mixed Numbers? Ans. Multiplying mixed numbers is a 3-step process: 1. Convert the mixed numbers to improper fractions 2. Multiply the fractions 3.
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