What is the set of O of odd positive integers less than 10?

Q: How many numbers between 1 and 10000 have the digits 1,3, and 5 such that each digit appears exactly…

A: Here Numbers between 1 and 10,000 have digits 1,3,5 and each appears exactly once only

Q: Jse a direct proof to show that if n² is an odd integer, then n* is also an odd integer.

A: Given, n² is an odd integer. So, n² = 2k+1, where k is an integer. Now, n⁴ = (n²)² = (2k+1)² = 4k² +…

Q: what two consective odd integers have a product of 63?

A: Find two odd integers.

Q: Justify that every prime number except 2 and 3 has the form 6q + 1 or 6q + 5 for some integer q.

A: Let ‘P ‘be any prime number Divide ‘p’ by 6, we get P=6q+r       - (1);     r=1,2,3,4,5 And q be any…

Q: prove the set of all irrational number between-6 and -4 is uncountable

A:

Q: Find the number of positive integers not exceeding 100 that are either odd or the square of an…

A: The objective is to find the number of positive integers not exceeding that are either odd or the…

Q: show that every integer greater than 11 is the sum of two composite integers

A: We need to prove that  every integer greater than 11 is the sum of two composite integers.

Q: Show that for all integers a, b > 0, the number (a + b) – (a O b) is both nonnegative and even.

A:

Q: 3. Show that there exist 100 consecutive positive integers that are not perfect squares.

A: Here we have to show that there exists 100 consecutive positive integer that are not perfect square.…

Q: Show that the set of odd numbers is countable.

A:

Q: What is the number of integers with (a) at most n (decimal) digits; (b) exactly n digits…

A: What is the number of integers with (a) at most n (decimal) digits; (b) exactly n digits (don’t…