Q/prove that:- An edge only if e e of agraph G is abridge if and is not part of any cycle in G.
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A: Statement to ProveFor all n ≥ 0: 1+2+22+⋯+2n=2n+1−1 Step 1: Base Case ( n = 0 )For n = 0:…
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- Let f and g be permutations on the set {1, 2, 3, 4, 5, 6, 7}, defined as follows (b) f-1 (c) fgf = f= = 9 = Write each of the following permutations as a product of disjoint cycles, separated by commas (e.g. (1, 2), (3, 4, 5), … ). Do not include 1-cycles (e.g. (2)) in your answer. (a) fg= 1 2 3 4 5 6 7 24 6 5 1 3 7 1 3 2 3 4 5 6 1 2 7 5 6 4 Assume multiplication of permutations f.g obeys the rule (fg)(x) = f(g(x)) so (1, 3) (1, 2) = (1, 2, 3) not (1, 3, 2).If B USES A, and A does not USE B, then which of the following statements is true: Relationship between A and B is asymmetric Change in B may require a change in A. Relationship between A and B is cyclic. Change in A may require a change in BShow that any k cyclically consecutive coordinate positions form an information set.
- Construct a preimage with vertices at (-7, 7), (-9, 3), (-3, 7), and (-5, 3). Create an image by reflecting this figure over the x-axis.Let x and y be two vertices of a Cayley digraph. Explain why twopaths from x to y in the digraph yield a group relation—that is, an equation of the form a1a2 . . .am =b1b2 . . .bn, where the ai’s andbj’s are generators of the Cayley digraph.8. If the graph of h(x) goes through the points A(-16,4), B(-4,0), C(0,-4) and D(4,16), then how many of the following statements are true for the graph of h(x) ? Point A will be mapped onto A'(-16,2). II. Point B will be an invariant point. III. Point C will be an invariant point. IV. Point D will be mapped onto D' (2,16) I. А. one B. two C. three D. four ZEBRA Mild Ink M IL DLI NER. -V5 А. V5 В. 5 2/5 С. - 2/5 D. Tiw doidw 10. If cos0 = V3 sin O then the exact value of tan 20 is: A. -V3 В. 2/3 D. 3 С.