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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
41x + 53y = 135, 53x +41y =147 Ans: 41x + 53 y = 135, 53 x + 41 y = 147 Add the two equations : Solve it, to get ... x + y = 3 -------(1) Subtract : Solve it , to
Short Cuts for solving quadratic equations
Brian's 100-yard dash time was 2.68 seconds more than one school record. Brian's time was 13.4 seconds. What is the school record? The school record is less than Brian's time.
a statisics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes. find the probability that a given class pe
one half y minus 14
How to Simplifying Square Roots ? To simplify square roots, 1. Factor the radicand into primes. 2. Circle each pair of like numbers. 3. For each pair of like numbers, place
Express the GCD of 48 and 18 as a linear combination. (Ans: Not unique) A=bq+r, where o ≤ r 48=18x2+12 18=12x1+6 12=6x2+0 ∴ HCF (18,48) = 6 now 6
Example: Find a general solution to the subsequent differential equation. 2 y′′ + 18 y + 6 tan (3t) Solution First, as the formula for variation of parameters needs coe
what is the ratio of sides of a right angle triangle which are in A.P
4x+8=32
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