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a) Using Karnaugh map, show
X': A'BC'D'+ ABC'D'+ A'BCD'+ ABCD' (b) If R is an equivalence relation on set A, prove that R-1 is also an equivalence relation.
(c) Explain Konigsberg's 7 bridges problem and Euler's solution to it.
Determine the linear approximation for f(x)= sin delta at delta =0
11-b=34
Two stations due south of a leaning tower which leans towards the north are at distances a and b from its foot. If α , β be the elevations of the top of the tower from these
Solve the subsequent proportion: Example: Solve the subsequent proportion for x. Solution: 5:x = 4:15 The product of the extremes is (5)(15) = 75. The produ
Q. Determine the probability of tossing a head? Let B represent the event of tossing a heads with the nickel in example 2. Find P(B). Solution: S = {(H, H), (H, T), (T, H
Equal groupings - when we want to find how many objects there are in several equal-sized sets. (e.g., if there are 3 baskets, each with 4 bananas, 4 oranges and 4 apples, respec
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
Let a, b, c 2 Z + . (a) Prove that if a|b, then ac|bc for all c. (b) If a|bc, can you conclude that either a|b or a|c? Justify your answer with a proof or a counter example.
Illustration : Solve the following IVP. Solution: First get the eigenvalues for the system. = l 2 - 10 l+ 25 = (l- 5) 2 l 1,2 = 5 Therefore, we got a
alpha and beta are concentric angles of two points A and B on the ellipse.
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