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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
y=f(a^x) and f(sinx)=lnx find dy/dx? Solution) dy/dx exist only when 0 1 as the function y = f(a^x) itself does not exist.
A jeweler has bars of 18-carat gold and 12-carat gold. How much of every melted together to obtain a bar of 16-carat gold, weighing 120 gm ? It is given that pure gold is 24 carat.
The temperature in Hillsville was 20° Celsius. What is the equivalent of this temperature in degrees Fahrenheit? This problem translates to the expression 3 {[2 - (-7 + 6)] + 4
What do you mean by transient state and steady-state queueing systems If the characteristics of a queuing system are independent of time or equivalently if the behaviour of the
In this section we will be searching how to utilize Laplace transforms to solve differential equations. There are various types of transforms out there into the world. Laplace tran
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Show that the product of 3 consecutive positive integers is divisible by 6. Ans: n,n+1,n+2 be three consecutive positive integers We know that n is of the form 3q, 3q +1
Logarithm Functions : Now let's briefly get the derivatives for logarithms. In this case we will have to start with the following fact regarding functions that are inverses of ea
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Example of line - Common Polar Coordinate Graphs Example: Graph θ = 3Π, r cos θ = 4 and r sin θ = -3 on similar axis system. Solution There actually isn't too much to
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