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Steps on Solving Discrete Questions

I need some help with this mathematical questions:
(a) Use the Binomial Theorem to write the expansion of (x + y) 6?
(b) Write the coefficient of the term x2y4z5 expansion of (x + y + z) 11.

Let A = {a, b, c, d}, and let R be the relation defined on A by the following matrix: (see attachment for
(a) Describe R by listing the ordered pairs in R and draw the digraph of this relation
(b) Which of the properties: reflexive, antisymmetric and transitive are true for the given relation? Begin your discussion by defining each term in general first and then how the definition relates to this specific example.
(c) Is this relation a partial order? Explain. If this relation is a partial order, draw its Hasse diagram.

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Solution Summary

The solution gives detailed steps on solving a couple of discrete questions. The topics include Binomial Theorem, coefficient of terms, reflexive property, anti-symmetric property, transitive property and partial order.