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Prove that the Digraph of a partial order has no cycle of length greater than 1.
Assume that there exists a cycle of length n ≥ 2 in the digraph of a partial order ≤ on a set A. This entails that there are n distinct elements a1 , a2 , a3 , ..., an like that a1 ≤ a2 , a2 ≤ a3 , ..., an-1 ≤ an and an ≤ a1 . Applying the transitivity n-1 times on a1 ≤ a2 , a2 ≤ a3 , ..., an-1 ≤ an , we get a1 ≤ an .As relation ≤ is anti-symmetric a1 ≤ an and an ≤ a1 together entails that a1 = an . This is contrary to the fact that all a1, a2, a3... an are distinct. So, our assumption that there is a cycle of length n ≥ 2 in the digraph of a partial order relation is wrong.
the cost of paint used in a redecorating job is $65.70 .This is a reduction from its original cost of $82.13 .What is the percent decrease in the cost of paint to the nearest perce
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Build a Fine Automaton which accept all words which have different first and last letters (that is if the word starts with an "a" to be accepted it should end with "b" and vice ver
The exponential functions are useful for describing compound interest and growth. The exponential function is defined as: y = m. a x where '
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just want to go over it
A and B can finish a piece of work in 16 days and 12 days respectively.A started a work and worked at it for 2 days.He was then joined by B.Find the total time taken to finish the
Find the x and y intercepts for the following equations: 3y=3x -y=-x-4 2x+3y=6 y=5
Interval of Convergence After that secondly, the interval of all x's, involving the endpoints if need be, for which the power series converges is termed as the interval of conv
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