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If f(x) and g(x) are two non-zero elements of F[x], then prove that deg [f(x)g(x)] = deg f(x) + deg g(x)
Prove that the polynomial x2 + x + 1 is irreducible over F, the field of integers modulo 2.
If zero cannot be used in the first position and repeats are allowed in the other 6 positions, how many license plates are possible?
How many ways can 5 Manchester United and 8 Chlesea players be seated at a circular dinner table if no two Manchester United players can sit together?
An airline has 15 flights from city A to city B and eight flights from city B to city C. In how many ways can you fly from city A to city B.
There are two small cities, Santa Clara and Santa Rosa. Santa Clara has 20 houses and Santa Rosa has 15 houses.
A set D is a subset of set C provided that?Provide complete and step by step solution for the question.
Eight people are attending a seminar in a room with eight chairs. In the middle of the seminar, there is a break and everyone leaves the room.
Find a complete set of mutually incongruent solutions. Provide complete and step by step solution for the question.
How many possible social security numbers are there if numbers can be repeated but 0 cannot be used for the first digit?
Preparing a plate of cookies for 8 children, 3 types cookies {chocolate chip, peanut butter, oatmeal}, unlimited amount of cookies in supply.
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