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Discrete Mathematics
Show that C (n+1, k) = C (n, k -1) + C (n, k)
Discrete Mathematics
Prove that
n*P( n -1,n - 1) = P (n, n)
Discrete Mathematics
If n fair six-sided dice are tossed and the numbers showing on top are recorded, how many
(a) record sequences are possible?
(b) sequence contain exactly one six?
(c) sequences contain exactly four twos, assuming n >= 4
Discrete Mathematics
Let A={1, 2, 3, 4} and R be the relation on A such that R = { (1, 2), (1, 4), (2, 1), (2, 3), (3, 1) }. Find the transitive closure of R by warshall's algorithm.
Discrete Mathematics
Let A={1,2,3,4,5} and R be the relation on A such that R={(1,1),(1,4),(2,2),(3,4),(3,5),(4,1),(5,2),(5,5)}. Find the transitive closure of R by Warshall's Algorithm
Discrete Mathematics
For each of the following relations, determine whether they are reflexive, symmetric, anti- symmetric, and/or transitive, and give a brief justification for each property. a) R ⊆ Z × Z where xRy iff x = y 2 b) The empty relation: R ⊆ A × A, where A is a non-empty set and R = ∅.
Discrete Mathematics
We are given two functions f : A → B and g : B → C. Prove that if f and g are onto, then g ◦ f is onto.
Discrete Mathematics
If n fair six-sided dice are tossed and the numbers showing on top are recorded, how many
(a) record sequences are possible?
(b) sequence contain exactly one six?
(c) sequences contain exactly four twos, assuming n 4 ?
Discrete Mathematics
Draw De Morgan’s Law, Absorption and Complementation Laws
Discrete Mathematics
Let A = {m, n, o}, B = {a, b}, and C = {7, 2}. Find: a) A x B x C. b) C x B x A. c) C x A x B. d) B x B x B.
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#340153 on Dec 2023
#340153 on Dec 2023