(8) How many integers in the set [1,000] = {1, 2, ..., 1,000} are (a) divisible by 5? divisible by 3? (b) divisible by 5 and divisible by 3? (c) divisible by 5 or by 3? (d) divisible by neither 3 nor 5? (e) divisible by exactly one of the numbers 3 or 5?

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

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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: What is the converse of: an integer has divisors other than 1 and itself, if an integer is…

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Q: Use the roster method to write the set of integers between 0 and 12

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Q: How many seven-digit numbers can be formed with the first two digits odd and the last five digits…

A: The total number of digits from 0 to 9 is 10.

Q: Using the digits 0,1,2,....8,9 determine how many of each type of the three-digit number can be…

A: Given digits 0, 1, 2, ............., 8, 9 Any three digit number with zero at its first place…

Q: How many integers in {1, 2,..., 100} are not divisible by 7 or 5? (Give the exact number)

A: Find the number of integers in 1,2,...,100 which are not divisible by 7 or 5.

Q: In a group of people, 68 people can speak English, 45 people can speak in Arabic and 19 people can…

A: It is given that 68 people can speak English, 45 people can speak Arabic and 19 people can speak…

Q: Find the number of positive integers not exceeding 104 that are not divisible by 5 or by 7.

A: In this Question we have to find the number of positive Integer between 0 and 104 which is not…

Q: How many positive integers less than 1000 are divisible by 5? How many positive integers less than…

A: We will answer the first three questions as per our guideline. Please resubmit the other question…

Q: How many positive integers less than 1000 (1) are divisible by 7? (2) are divisible by 7 but not by…

A: # As per the guidelines we are entitled to solve three subparts at a time, please resubmit the other…

Q: How many integers in {1,2, 3, ..., 99, 100} are not divisible by 7? (Give the exact number)

A: The given set of numbers is, 1,2,3,.....,99,100 The total no.of numbers from 1 to 100 is, 100 The…

Q: 3. Prove or disprove [yes, these should look familiar from §2.3]: (a) The sum of three consecutive…

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Q: (a) Suppose that there are k distinct positive integers that divide an odd positive integer n.…

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Q: How many three digit numbers (values between 100 and 999 inclusive) are divisible by four? How many…

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