How many 98-element subsets does [100] have? (Here [100] is the set consisting of the first 100 positive integers). Hint: This should not be a lengthy computation.

Q: The representation of an even integer is 2k; and that for odd is 2k+1 or 2k-1 for some integer k.…

A: To show the representation of an even integers is 2k and that for odd integer is 2k+1 or 2k-1 by…

Q: How many integers from 1 to 700 (inclusive) are divisible by the factors of 70 greater than 1?

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Q: Explain why, in any set of 11 positive integers, some two integers must have the same I's digit.

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Q: Suppose 35 cars start at a car race. In how many ways can the top 3 cars finish the race?

A: The information provided in the question are as follows :-There are  cars at a car race.

Q: If A is the set of all whole numbers less than 20 that are divisible by, 4, and B is the set of all…

A: A∪B is the union of set A and set B. This set contains all the elements in set A or set B. The Venn…

Q: Show that 2N, the collection of all sets of natural numbers, is uncountable.

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Q: Compute for an arbitrary integer k

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Q: The representation of an even integer is 2k; and that for odd is 2k+1 or 2k-1 for some integer k.

A: integer  which have 2 as one of their factors are called even numbers. The integer  which do not…

Q: The number of integers between 1 and 500 (both inclusive) that are divisible by 3 or 5 or 7 is

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Q: 1 101101, and 101, 2. 10111102 and 102 and 112 3. 1000012

A: Since there are multiple questions the first question is answered as per our guidelines. Kindly…

Q: Texas is starting a lottery game. Play- ers use a machine that randomly selects 7 distinct numbers…

A: To calculate the probability that Texas will lose money, we need to determine the expected value of…

Q: 5. (12 points) Find how many positive integers between 1 and 99, inclusive, have the following…

A: The objective of this question is to find the number of positive integers between 1 and 99 that…

Q: Let Sbe the set of all (nonnegative) 4-digit integer. How many integers from start with 1 and end…

A: let S be the set of all 4-digit integer. how many integers from start 1 and end with 9

Q: How many people only cycled if 1978 took public transit, 1494 drove, 818 cycled, 731 took public…

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Q: A multiset is similar to a set, but can contain an element more than once. How many multisets can we…

A: You can identify every multiset with an ordered pair of usual sets, call them high and low. If you…

Q: Suppose that a password is exactly six characters and each character is 1 of the 26 lowercase…

A: The number of lowercase letters is 26 and the number of integers is 10.

Q: How many elements are there in the greatest conjugacy class of 5 ?S

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Q: 1) Find two distinct ways to write the even integers using set-builder notation. 2) Then, find…

A: 1 Two distinct ways to write the even integers using set-builder notationWay 1:  x  x=2n, n∈Z Way 2:…

Q: How many integers between 1000 and 9999 inclusive are not divisible by 5?

A: The number of integers from 1 and 9999 which are divisible by 5 is = [9999 ÷ 5] = [1,999.8] = 1999…

Q: Use induction to prove that the product of any three consecutive positive integers is divisible by…

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Q: Suppose 59 cars start at a car race. In how many ways can the top 3 cars finish the race? ... The…

A: There is total 59 cars.

Q: Prove that if the sum of the digits is subtracted from a natural number, then the result is…

A: let us assume the number to be three digit number xyz therefore, xyz=100x+10y+z sum of digits will…

Q: identify all natural numbers having exactly 28 divisors.

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Q: Assume that all four-digit integers (numbers from and including 1000 to and including 9999) are…

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Q: Recall that hexadecimal numbers are constructed using the 16 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A,…

A: We know that,Hexadecimal numbers are constructed using the 16 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,…