Reference no: EM13131975
Let A and B be sets. Show that A x B and B x A have equal cardinality by constructing an explicit bijection between the two sets. Then use the following proposition to prove that multiplication is commutative. (Let n, m be natural numbers. Then nxm=mxn)
Proposition: Cardinal arithmetic
a) Let X be a finite set, and let x be an object which is not an element of X. Then X U (union) {x} is finite and #(X U {x})= #(X)+1
b) Let X and Y be finite sets. Then X U Y is finite and # (X U Y) is less than or equal to #(X) + #(Y). If in addition X and Y are disjoint (i.e., X intersection Y = the empty set), then #(X U Y)= #(X) + #(Y)
c) Let X be a finite set, and let Y be a subset of X. Then Y is finite, and #(Y) is less than or equal to #(X), If in addition Y does not equal X (i.e. Y is a proper subset of X), then we have #(Y) is less than #(X)
d) If X is a finite set, and f:X-->Y is a function, then f(X) is a finite set with #(f(X)) less than or equal to #(X). If in addition f is one to one, then #(f(X)) = #(X)
e) Let X and Y be finite sets. Then cartesian product X x Y is finite and # (X x Y) = #(X) x #(Y)
f) Let X and Y be finite sets. Then the set Y^X is finite and #(Y^X)= #(Y)^#(X)
|
Expected return with a standard deviation
: Security A has an expected return of 12.4% with a standard deviation of 15%, and a correlation with the market of 0.85. Security B has an expected return of 0.73% with a standard deviation of 20%, and a correlation with the market of 0.67. The sta..
|
|
Probability that the mean of a sample families is in range
: Assume the standard deviation of the distribution is 2.5pounds, what is the probability that the mean of a sample of 55 families is between 17 and 18 pounds.
|
|
Proof regarding set theory
: Let A, B, C be sets and let X be a set containing A, B, C as subsets. Prove that A intersects (B union C)= (A intersects B) union (A intersects C)
|
|
By how much could advertising be increased with profits
: Feather Friends, Inc., distributes a high-quality wooden birdhouse that sells for $24 per unit. Variable costs are $10.80 per unit, and fixed costs total $174,000 per year.
|
|
Information about proof about cardinality
: Let A and B be sets. Show that A x B and B x A have equal cardinality by constructing an explicit bijection between the two sets. Then use the following proposition to prove that multiplication is commutative. (Let n, m be natural numbers. Then nx..
|
|
What gain must father recognize in 2012
: In 2011, Father sold land to Son for $150,000 cash and an installment note for $450,000 due in 2015. Father's basis was $240,000. In 2012, after paying $27,000 interest but nothing on the principal, Son sold the land for $600,000 cash. As a result..
|
|
Estimate relative risk for reduction in the symptom
: Generate a 95% CI for the difference in proprotions of particpants reportinga reduction of symptoms between the experimental and placebo groups.
|
|
What amount it report as cumulative effect of changing
: Vandross Company has recorded bad debt expense in the past at a rate of 1.5% of net sales. In 2012, Vandross decides to increase its estimate to 2%.
|
|
Why is cost accumulation simpler in a process costing system
: Why is cost accumulation simpler in a process costing system than it is in a job-order costing system?
|