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Discrete Mathematics
A trade development board organized coventions abroad for its 150 members in the jewelers industry. The coventions fell under three categories trading, manufacturing and design 52 attended the trading category, 46 the manufacturing and 32 the design; 20 attended the trading and manufacturing category and 18 the trading and design; 8 attended the manufacturing and design but not the trading category and 14 attended the trading and manufacturing but not the design category. draw a venn diagram to illlustrate the above information and find the number of members who attended
i. none of the convention
ii. at least two categories of the coventions
iii. akk the three categories of the conventions.
i. none of the convention
ii. at least two categories of the coventions
iii. akk the three categories of the conventions.
Discrete Mathematics
Let G be a simple graph with 20 vertices and 100 edges. The size of the minimum vertex cover of G is 8. Then size of the maximum independent set of G is
a) more than 12
b) less than 8
c) 8
d) 12
a) more than 12
b) less than 8
c) 8
d) 12
Discrete Mathematics
What is the number of perfect matching of a complete graph Kn with n vertices?
Discrete Mathematics
Consider the following two problems on undirected graphs:
α: Given G(V,E), does G have an independent set of size |v|—4?
β: Given G(V,E), does G have an independent set of size 5?
Which one of the following is TRUE?
a) α is in P and β is NP-complete
b) α is NP complete and β is in P
c) Both α and β are NP-complete
d) Both α and β are in P
α: Given G(V,E), does G have an independent set of size |v|—4?
β: Given G(V,E), does G have an independent set of size 5?
Which one of the following is TRUE?
a) α is in P and β is NP-complete
b) α is NP complete and β is in P
c) Both α and β are NP-complete
d) Both α and β are in P
Discrete Mathematics
What is the number of elements in the smallest equivalence relation over set A with |A|=n ?
Discrete Mathematics
Let S be a set of n elements. The number of ordered pairs in the largest and the
smallest equivalence relations on S are:
(A) n and n (B) n^2 and n (C) n^2 and 0 (D) n and 1
smallest equivalence relations on S are:
(A) n and n (B) n^2 and n (C) n^2 and 0 (D) n and 1
Discrete Mathematics
What is the number of perfect matchings of K6? Explain.
Discrete Mathematics
A graph G and its complement G have 8 and 7 edges respectively. What is the
number of vertices in G ?
number of vertices in G ?
Discrete Mathematics
Find the transitive closure of R = {(a, a), (b, a), (b, c), (c, a), (c, c), (c, d), (d, a), (d, c)} on the set {a, b, c, d}.
Discrete Mathematics
a)Consider the decimal number a = 137.
i.Find in set builder notation the set of all positive integers b such that b ≡ a (mod 5).
ii.Is the number a prime? Explain.
iii.Convert the number a to binary and octal numbers
i.Find in set builder notation the set of all positive integers b such that b ≡ a (mod 5).
ii.Is the number a prime? Explain.
iii.Convert the number a to binary and octal numbers
