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Discrete Mathematics
Let A,B,C єR2 where A = { (x,y) / y = 2x + 1} , B = { (x,y) / y = 3x} and C = { (x ,y) / x - y = 7} . Determine each of the following:
i. A B ii. B intersection C complement 3.
i. A B ii. B intersection C complement 3.
Discrete Mathematics
If R is a relation defined on the set Z by a R b if a-b is a non negative even integer. Determine if R define a partial order and total order.
Discrete Mathematics
Let f and g be functions from the positive real numbers to positive real numbers defined by f(x) = [2x]
g(x) = x2. Calculate f o g and g o f.
g(x) = x2. Calculate f o g and g o f.
Discrete Mathematics
Define a bijective function. Explain with reasons whether the following functions are bijective or not. Find also the inverse of each of the functions.
i. f(x) = 4x+2, A=set of real numbers
ii. f(x) = 3+ 1/x, A=set of non zero real numbers
iii. f(x) = (2x+3) mod7, A=N7
i. f(x) = 4x+2, A=set of real numbers
ii. f(x) = 3+ 1/x, A=set of non zero real numbers
iii. f(x) = (2x+3) mod7, A=N7
Discrete Mathematics
Draw the Hasse diagram for the “divides” relation on {2, 3, 5, 10, 11, 15, 25, 36, 42, 108}
Discrete Mathematics
Determine whether each of these functions is a bijection from R to R?f (x) = (x2 + 1)/(x2 + 2)
Discrete Mathematics
Find the transitive closure A={1,2,3,4,5}
R={ (2,3),(3,5),((1,2),(2,5),(1,3),(4,5),(5,2)} by using Warshall’s Algorithm.
Discrete Mathematics
Find these terms of the sequence (An}, where An = 2(3)n + 5
Discrete Mathematics
a recursive function is defined by can=2an-1 with a0=1. find the value of a3
Discrete Mathematics
Show that ¬ (P"\\iff"Q)"\\iff"(P V Q) Λ ¬(P Λ Q) "\\iff"(P Λ ¬Q) V (¬ P Λ Q) without using truth table
