Is the set O of all odd counting numbers (1, 3, 5… ) closed for multiplication? Why or why not?

Q: Produce the least positive number that is divisible by​ 2, 3,​ 4, 5,​ 6, 7,​ 8, 9,​ 10, and 11.…

A: Given Produce the least positive number that is divisible 2, 3,​ 4, 5,​ 6, 7,​ 8, 9,​ 10, 11.…

Q: Prove: The sum of an odd number of odd numbers must be odd.

A: Let us prove this by induction, that if n is odd and a1,a2,. . .. .an are odd, then ∑i=1nai is odd.…

Q: 10(c) Suppose a set of 8 numbers are selected from the set {1,2,...,13,14}. Show that two of the…

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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: How many subsets are there of the set N = {5, 42}?

A: We ahave to find no. Of subsets.

Q: Using the set {1,3,4,6,7,8,9}, how many odd numbers can we construct between 100-999 if no element…

A: An odd number is determined by the unit digit. If the unit digit is an odd number, then the number…

Q: A PIN-number for a credit card consists of a sequence of 4 digits chosen from the set…

A: Given the set {0,1,2,3,4,5,6,7,8,9} We find the 4 digits different PIN number

Q: A. How many 3 digit numbers greater than 200 can be made from 0,1,2,3,4,5 if repetition of digits is…

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Q: 1. How many ways can you choose 4 numbers from the set p = {4, 6, 8, 10, 12} or 3 numbers from the…

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Q: Two distinct numbers are selected from the set {1, 2, 3, 4, . , 36, 37} so that the sum of the…

A: Distinct number: The term distinct number is used to refer to a number in a set that is not equal to…

Q: How many subsets are there of the set N = {6, 49}?

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Q: (A) For what values of a in (0,8) is f(x) concave down? (If the function is not concave down…

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Q: Find the largest eight-digit number made up of the digits 1, 1, 2, 2, 3, 3, 4, and 4 such that the…

A: Given digits are 1,2, 3, 4.Given conditions is 1s are seperated by one digit,2s are seperated by two…

Q: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 8 and 9, which are divisible by 5…

A: From the given Numbers we have to form 3 digit numbers the digits are 2, 3, 5, 6, 7, and 9, which…

Q: How many four-digit odd numbers less than 5000 can be formed using the digits 2, 3, 4, 5, 6. 6, and…

A: Now here given  digits 2,3,4,5,6,9

Q: Consider the list of numbers: 2n-1, where n first equals 2, then 3, 4, 5,6,…What is the smallest…

A: Given that, A numver is, 2n - 1 Where n = 2, 3, 4, 5, 6, 7, ............ We have to find the…

Q: 1) Find the number of positive integers not exceeding 100 that are not divisible by 5 or

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