Q-2: [4+4 marks ] a) Define A△B=(A−B)∪(B−A) , where A,B are any two sets. Show that (AΔB)ΔC=AΔ(BΔC) b) Prove or disprove: i. ⌈x⌉=−⌊x⌋ . ii. For all positive real numbers x and y,⌊x⋅y⌋≤⌊x⌋⋅⌊y⌋ .
EXPERT ANSWER
Determine whether each of the following is true or false. If true, prove the statement. If false, find a counterexample. a) For all integers a, b,and c, if a | b and a | c then a | (3b − 5c). b) For all integers a ≥ 4 and b, if a | 3b then …
Write the function in the form f (z) = u (x,y) + iv (x,y) and find all points where the Cauchy-Riemann equations are satisfied EXPERT ANSWER
Suppose our stream consists of the integers 3, 1, 4, 1, 5, 9, 2, 6, 5. Our hash functions will all be of the form h(x) = ax+b mod 32 for some a and b. You should treat the result as a 5-bit binary integer. Determine the tail length for each stream element and the …
Consider the pattern P=a3ba. Construct the table and the corresponding labeled directed graph used in the “fast” pattern matching algorithm EXPERT ANSWER
EXPERT ANSWER Let gcd(a,b,c) = m.Therefore, m divides a, b and c.Then, gcd(a,b) = mx, gcd(b,c) = my, gcd(a,c) = mz where x, y, z are all greater than or equal to 1. Thus, gcd(a,b)xgcd(b,c)x gcd(a,c) = mxmymz = xyzm3 And [gcd(a,b,c)]3 = m3. xyzm3 is greater than or equal to m3 Therefore, gcd(a,b)xgcd(b,c)x gcd(a,c) …