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Define spanning trees in a weighted graph, with an example
Show that every simple finite graph has two vertices of the same degree
Write short note on Caesar cipher with example
Describe any three inference rules
1a) Use set-builder notation to prove that
A-(B ∩C)=(A-B)∪(A-C)
b) Let E={ 1,23,4,5,6,7,8,9,10} and ordering of element in increasing order that is a= i; what bit strings represent the subsets of integers not exceeding 5 in E
3a)Let A={1,2,3},determine all partitions of A
1. Classify and compare the different types of antenna using ah venn diagram. Discuss each type in each petal of the diagram.
Construct a K-map for F(x, y, z) = xz + yz + xyz. Use this K-map to find the implicants, prime
implicants, and essential prime implicants of F(x, y, z).
Let A = {2, 4} and B = {2, 4, 6} and define a relation R for A to B as follows:
Question: Which ordered pairs belongs to relation R?
A gumball machine contains 300 grape flavored balls, 400 cherry flavored balls, and 500 lemon flavored balls. What is the probability of getting 1 grape ball, 1 cherry ball, and 1 lemon ball if each ball was removed and then replaced before choosing the next from the machine?
Show that if n is a positive integer with n ≥ 3, then
C(n, n − 2) = ((3n − 1)C(n, 3))/4
