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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
Find the ratio in which the line segment joining A(6,5) and B(4,-3) is divided by the line y=2 (Ans:3:5) Ans : Let the ratio be k:1 x = 4 k + 6/ k +1 y
Find the probability of drawing a diamond card in each of the two consecutive draws from a well shuffled pack of cards, if the card drawn is not replaced after the first draw
Prove that a reaction following the rate law v = k[A] 2 is characterized by a linear plot of [P] t 1 versus t-l, where P is the product of the stoichiometric reaction A = P. Sho
Write each of the given radicals in exponent form. Solution As illustrated in the last two parts of this example we have to be careful with parenthesis. While we
a) Let n = (abc) 7 . Prove that n ≡ a + b + c (mod 6). b) Use congruences to show that 4|3 2n - 1 for all integers n ≥ 0.
degree of a diffrential equation
Venn Diagram - Set theory and calculus A easy way of representing sets and relations among sets is by means of the Venn diagram. Venn diagram includes of a rectangle that pres
10 statements must be shown to be logically equivalent to the Statement the nxn matrix is invertible.
1. Let A = {1,2, 3,..., n} (a) How many relations on A are both symmetric and anti-symmetric? (b) If R is a relation on A that is anti-symmetric, what is the maximum number o
DEVELOPING PRE-NUMBER CONCEPTS : Previously you have read how children acquire concepts. You know that, for children to grasp a concept, they must be given several opportunities
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