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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
One of the simplest physical situations to imagine of is a falling object. Thus let's consider a falling object along with mass m and derive a differential equation as, when resolv
Verify Liouville''''s formula for y "-y" - y'''' + y = 0 in (0, 1) ?
If A & B are (-2,-2) and (2,-4) respectively, find the co ordinates of P such that AP =3/7 AB and P lies on the line segment AB.
3x+5y
i needed help with algebra
Computing Limits :In the earlier section we saw that there is a large class of function which allows us to use to calculate limits. However, there are also several limits for whi
what is the value of zero to the power raised to zero?
a) Determine the distance traveled among t = 0 and t =∏/2 by a particle P(x, y) whose position at time t is given by Also check your result geometrically. (5) b) D
Example Multiply 3x 5 + 4x 3 + 2x - 1 and x 4 + 2x 2 + 4. The product is given by 3x 5 . (x 4 + 2x 2 + 4) + 4x 3 . (x 4 + 2x 2 + 4) + 2x .
The angles between three non-zero and non coplanar vectors a,b and c are α between b and c and β between c and a and γ between a and b. The vector u and v are defined by u=(aX
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