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1) Find a relation R on a set S that is neither Symmetric nor antisymmetric
2) Let S be a set containing exactly n elements. How many antisymmetric relations on S are there.
3) give a recursive definition of X^n for any positive integer n
4) give a recursive definition of the nth odd positive integer
5) Let g: Z -> Z be defined by g(x)= ax + b, where Z denotes the set of integers and a,b E Z with a not equal 0
a) prove that g is one-to-one
b) what must be true about a and b if g is onto?
6) let S be a set of people. For x, y E S, define xRy to mean that x = y or x is a decendant of y. Prove that R is a partial order on S
Simplifying the expression.
A shopper buys three oranges and five lemons for $10.26, while a second shopper buys four lemons and six oranges for $11.16. What is the price of each fruit?
Solve the following.
Make an equation of the line with a slope of two
f has a so-called "removeable singularity" at x=0, where it is (so far) undefined. What value should we assign to f(0) to make f continuous at x=0?
Suppose that you need a loan of $160,000. find the total cost of all the monthly payments for the loan below. assume that the loans are fixed rates.
Explain why T has at least one eigenvalue. We will denote this eigenvalue by λ.
Show that the trace is a linear map of the space of n n matrices into K.
From the matrix S who columns are the three vectors in your basis for E3, and compute J = (S^-1)AS. Notice that if you order the columns of S in the most logical way, J will be triangular.
questionaccountants as information keepers and produce financial reports to stakeholders face major ethical challenges
Solve these questions in detail - Domains of Rational numbers.
Solving the equation and rationalizing the denominator
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