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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
The vertices of a ? ABC are A(4, 6), B(1. 5) and C(7, 2). A line is drawn to intersect sides AB and AC at D and E respectively, such that AD/AB = AE/AC = 1/4 .Calculate the ar
what is 8x6 is
Example of Trig Substitutions Evaluate the subsequent integral. ∫ √((25x 2 - 4) / x) (dx) Solution In this type of case the substitution u = 25x 2 - 4 will not wo
Rick is order a latest triangular sail for his boat. He needs knowing the area of the sail. Which formula will he use? The area of a triangle is 1/2 times the length of the bas
sin(xy)+x=5y Find the derivative.
Maths For Fun : Often, when I have time on my hands, I try to solve interesting mathematical questions of the following kind. Sometimes my friends and I create the problems, and
Speaking Mathematically : A Class 2 teacher was explaining the concept of place value to his students, using the number eleven. He started by saying "One and one make eleven." So
Rules Of Game Theory i. The number of competitors is finite ii. There is conflict of interests among the participants iii. Each of these participants has available t
Circles - Common Polar Coordinate Graphs Let us come across at the equations of circles in polar coordinates. 1. r = a . This equation is saying that there is no matter
Find out the surface area of the solid acquired by rotating the following parametric curve about the x-axis. x = cos 3 θ y = sin 3 θ 0 ≤ θ ≤ ?/2 Solution We wil
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