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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
Rule 1 The logarithm of 1 to any base is 0. Proof We know that any number raised to zero equals 1. That is, a 0 = 1, where "a" takes any value. Therefore, the loga
Explain Combining Negative Signs in integers? You've learned about positive and negative integers. BASICS : When you place a negative sign in front of an integer, you get
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Fermat's Theorem If f(x) has a relative extrema at x = c and f′(c) exists then x = c is a critical point of f(x). Actually, this will be a critical point that f′(c) =0.
A solution to a differential equation at an interval α Illustration 1: Show that y(x) = x -3/2 is a solution to 4x 2 y′′ + 12xy′ + 3 y = 0 for x > 0. Solution : We'll
Compute the volume and surface area of a right circular cone: Compute the volume and surface area of a right circular cone along with r = 3", h = 4", and l = 5". Be sure to
Example: Suppose your football team has 10 returning athletes and 4 new members. How many ways can the coach choose one old player and one new one? Solution: There are 10 wa
Consider the clique graph below. a) How many subgraphs of G with 3 nodes are there? b) How many of the subgraphs defined in part(a) are induced subgraphs?
Find out the volume of the solid obtained by rotating the region bounded by y = x 2 - 2x and y = x about the line y = 4 . Solution: Firstly let's get the bounding region & t
PLAY AND LEARN : Children can learn many basic mathematical concepts through games. They enjoy Mathematical concepts can be playing within familiar contexts. Their games also gen
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