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For the metric space { N }, the set of all natural numbers, characterize whether or not it has the following properties.
An automobile license number contains 1 or 2 letters followed by a 4 digit number. Compute the maximum number of different licenses.
Describe precisely the set {sigma * (1, 2, . . . , k) * sigma-inverse | sigma is an element of Sn}.
Joey is having a party. He has 10 friends, but his mom told him he could only invite 6 of them. How many choices are there if there are no restrictions
Show that the following set is infinite by setting up a one-to-one correspondence between the given set and a proper subset of itself: {8,10,12,14,...}
How does this relate to the concept of counting the number of outcomes based on whether or not order is a criterion?
Imagine you've been left in charge of an ice cream stall and you have three flavours of ice cream to sell - vanilla, strawberry and chocolate.
Describe their usefulness and how businessman can be benefit, or how to help them in making sound decisions. (Explain individually).
If you have six pairs of jeans, three shirts and two pairs of sandals, how many different outfits can you wear?
I have two random walks, both starting at 0 and with a reflecting boundary at 0. Each Step, Walk A goes up 1 with probability 1/2.
Suppose that two of her friends (of the 14 of either gender) do not like each other. If one of the two is invited, the other will not come to the party.
How many different license plate numbers can be made using 2 letters followed by 4 digits selected from the digits 0 through 9.
Out of 30 job applicants, 11 are female, 17 are college graduates, 7 are bilingual, 3 are female college graduates, 2 are bilingual woman.
Which of the following statements is true? A intersection of B is the subset of A
Suppose that R and S are two relations on the set A = {a, b, c, d}, where R = {(a,b),(a,d),(b,c),(c,c),(d,a)}, and S = {(a,c),(b,d),(d,a)}.
A person has 3 different letters to write, 2 interviews to do, and 2 commercials to review.
Find the exponential generating function for Sn,r the number of ways to distribute r distinct objects into n distinct boxes with no empty box.
Definition: For any E in X, where X is any set, define M(E) = infinity if E is an infinite set, and let M(E) be then number of points in E if E is finite.
Show that if A is equivalent to B and C is equivalent to D, then A x C is equivalent to B x D.
If there are 10 students who own both a cellphone and a digital tv, but not a laptop, and there are 20 students who don't own a cellphone.
A computer lab contains the following computers – a Hewlett Packard, a Compaq, a Sony, a Dell and 3 different models of Macs.
Show that if 7 integers are selected from the first 10 positive integers there must be at least 2 pairs of these integers with the sum 11.
Find the condition for the modulus n, for which the congruence 2x+6 = 4 (mod 8) actually does have the solution set {x; x = -1 (mod 8)}.
Write the given permutation as the product of disjoint cycles. Provide complete and step by step solution for the question.
Let Y=(u v/u^4=v^3=1,uv=u^2v^2) show that u=1, deduce that v=1 and conclude that Y=1