Ali is student who can find all words that can be read the same forward and backward. He could not teach other students how they can found that words.
Inductive Hypothesis Discrete Mathematics Questions
Q1: Marks: 40 a) Ali is student who can find all words that can be read the same forward and backward. He could not teach other students how they can found that words. Solve problem by using an algorithm for determining whether a word of n characters is can be read same forward and backward. b) Prove that 12 -22 +32 -.– +(-1)n-n2 = (-1) + n(n+1)/2 whenever n is a positive integer.
Q2: Marks: 20 Construct graph models, stating the type of graph used, to represent Oman airline routes where every day there are four flights from Masuct to Salalah, two flights from Salalah to Masuct, three flights from Salalah to Suhar, two flights from Suhar to Salalah, one flight from Salalah to Kasab, two flights from Kasab to Salalah, three flights from Salalah to Doqom, two flights from Doqom to Salalah, and one flight from Doqom to Suhar, with: i. An edge between vertices representing cities that have a flight between them (in either direction) ii. An edge between vertices representing cities for each flight that operates between them (in either direction). iii. An edge between vertices representing cities for each flight that operates between them (in either direction), plus a loop for a special sightseeing trip that takes off and lands in Suhar. iv. An edge from a vertex representing a city where a flight starts to the vertex representing the city where it ends. e) an edge for each flight from a vertex representing a city where the flight begins to the vertex representing the city where the flight ends.
Q3: Marks: 40
a) Construct an order rooted tree for your family contain your parent, sibling, ancestors and descendants. Apply Breadth-first searching and Depth-first searching to find your name.
b) Construct a circuit using AND gates, OR gates, and inverters that has as input the four electrical signal Y1, Y2, Y3, and Y4 and the two electrical signal coming from other circuit represent by U1 and U2 by using below Boolean expression: i. (?1+Y2)(Ï3Ý4)+(0102)
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