True or false All fractions are real numbers- The elements of prime numbers are odd number- Composite numbers and prime numbers have elements in common- Real number is a part of integers - All integers are natural numbers-

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…

A:

Q: How many 3-digit positive integers exist that when divided by 7 leave a remainder of 57

A: 3 digit positive integers start from 100 and ends with 999. Least positive 3 digit integer which…

Q: The operation subtraction on the set of natural numbers N.

A:

Q: Every natural number can be written as the products of prime numbers

A: Prime numbers are the numbers which have only two factors, 1 and the number itself.

Q: Prove that 5 does not divide 5n+3 for any integer n.

A:

Q: How many natural numbers that are less or equal to 1000 and that are not multiples of 3, 5, or 7…

A: A number is said to be divisible by other number if on dividing the number  with it given remainder…

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: ll integers are rational numbers

A: All integers are rational numbers

Q: How is duality connected to the principle of reciprocity in number theory?

A: To find: How is duality connected to the principle of reciprocity in number theory.Duality and the…

Q: Every natural number can be written as the products of prime numbers

A: This statement is true and we can prove this in step 2.

Q: The number 42 has the prime factorization 2- 3-7. Thus, 42 can be written in four ways as a product…

A: Factorise  910 inti prine factors and the find the required pairs.

Q: noosing a positive integer from 100 to 999, what is the poSSibility of choosing a positive integer…

A:

Q: 57 + 233+ 43+ 67 Use commutative property to switch two of the numbers to make it easier to add…

A: The given addition can be written as (57+43)+(233+67).

Q: Some integers are whole numbers

A:

Q: Show that given any set of 5 natural numbers, there are 3 numbers whose sum is divisible by 3.

A: Let q∈N. Note that, for every q there exists some x∈N and some v∈0,1,2 such that q=3x+v. Now, let…

Q: How many ways are there to write a 3-digit positive integer using the digits 1, 3, 5, 7, and 9 if no…

A: The given digits are: 1, 3, 5, 7, and 9. We have to find the number of ways to write a 3-digit…

Q: Describe a general method for finding all the divisors of a positive integer once you know the prime…

A: Given  A positive Integer whose prime factorization is given . To find all the divisors with general…

Q: identify all natural numbers having exactly 28 divisors.

A:

Q: What is the smallest subset of real numbers -4 fits into?

A: Understanding of the number system is required in order to solve this question. The real numbers are…

Q: 12 belongs to the set of natural numbers

A: The natural numbers (i.e. counting numbers) are numbers which are used for counting and ordering.…

Q: Prove that 4 does not divide n2 +2 for any integer n.

A:

Q: True/False: Every integer greater than 1 is divisible by a prime number. True False

A:

Q: How many real four digit numbers (they can not start with zero) can be formed from digits 0, 1, 2,…

A: Given digits is 0,1,2,3,4,5,6Total no.of digits = 7

Q: Is multiplication a binary operation on the set of rational number? If yes, why? If no, explain and…

A: Rational numbers are numbers that can be expressed in the form of pq, where p and q are integers.…

Q: Consider the set of rational numbers under the operation of addition. What is the inverse of 9?

A: