Let A be the set of positive integers that are less than or equal to 40 and are multiples of 4 and let B be the set of positive integers that are less than or equal to 40 and are multiples of 6. Determine the number of elements in AUB?

Q: How many integers between 100 and 400 contain the digot 2?

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Q: Suppose we define a function f(x) by f(x) = a1 sin(x) + a2 sin(2x) +· + an sin(nx), .. for constants…

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

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Q: How many integers from 1 through 1000 are multiples of 7 or multiples of 4?

A: Let A be the set of integers that are multiples of 7 and B be the set of integers that are multiples…

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

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Q: How many 5 digit even numbers are there, a. Given that the first digit cannot be zero. b. Given…

A: In five digit following digit can be filled in following ways: First digit can be filled by…

Q: Select 8 different numbers from {1, 2, 14). Show that you can find at least three pairs of numbers…

A: To show that you can find at least three pairs of numbers with the same positive difference from the…

Q: The principal of a college wishes to introduce three new evening classes. The classes are Cake…

A: Venn diagram is a graphical representation of datasets or the probability of events. An event in the…

Q: A drawer contains 10 red socks, 10 blue socks, 10 green socks, and 10 yellow socks. What is the…

A: Given : red socks = 10 blue socks = 10 green socks = 10 yellow socks = 10

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 are…

Q: let a,b,c,d,e and f be different positive integers so that a² - b² = c² - d² = e² - f² = 63. Value a…

A: Given:- a,b,c,d,e and f are different positive integers.  also a2-b2=c2-d2=e2-f2=63. To find :- the…

Q: a) Find the number of positive integers not exceeding 120 that are divisible by 3 or 4.

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Q: 3. Let A = 3-1 1 V₁ = 3 -2 2 = 2 V₂ = 3 V3 = 6 V4 and use the facts Av₁ = V₁ AV₂ = V₂ AV3 = V3 V4 €…

A: 3. Let , and use the facts  to answer the following question.(c) If A is diagonalizable then give…

Q: A drawer contains 10 red socks, 10 blue socks, 10 green socks, and 10 yellow socks. What is the…

A: To guarantee that the drawer no longer contains any red socks, you need to remove all the socks 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: Find the g.c.f. and l.c.m. of the set of numbers. {2, 4, 10, 36} g.c.f.       l.c.m.

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Q: How many 3-digit number can be formed from the digits 0,1,2,3  a. if no two digits are to be the…

A: * SOLUTION :-  from the given information the calculation is given below

Q: "find A2, A−2, and A−k (where k is any integer) by inspection."

A: NOTE: Refresh your page if you can't see any equations. . use the diagonal matrix formula

Q: let a, b, c, d, four consecutive positive numbers show that g.c.d (a, b, c, d)=1

A: Given :- a, b, c, d, four consecutive positive numbers. As a,b,c,d are consecutive positive numbers…

Q: - Let a, b, n be positive integers. Prove that if a = b (mod n), then (a, n) = (b, n).

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Q: Using the digits 0 through 9, find out how many 4-digit numbers can be configured based on the…

A: The fundamental counting principle says that if there are n ways to choose something and m ways to…

Q: Find the number of different 7-digit numbers which can be formed from the seven digits 4, 4, 7, 9,…

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Q: Determine which positive integers ? have a. Exactly 2 positive divisors b. Exactly 4 positive…

A: A positive integer has exactly 2 positive divisors if and only if it is a prime number.

Q: a. On each of four consecutive plays in a football​ game, a team lost 8 yards. If lost yardage is…

A: On each of  four consecutive Plays in football gane team lost 8 yards

Q: A drawer contains 10 red socks, 10 blue socks, and 10 green socks. What is the minimum number of…

A: 10 socks of each colour Red, Blue and Green. the maximum number of socks we can take out of the…

Q: How many negative divisors has the integer 90?

A: The divisors of 90 are all the numbers that we can evenly divide into 90.

Q: Determine if 3 is in Nul A, where 3 -5 -3 6 -2 -8 4

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Q: that the set of negative integers divisible by 3 is countable

A: Set of negetivee integers divisible by 3 isS=-3n, n∈ℕf: ℕ→S   defined asf(n) = -3n,To check…

Q: Find the number of positive integers ≤ 1000 that are not divisible by 5, 13, or 31?

A: .  Symbol of Greatest Integer Function  To Find: Number of positive integers ≤ 1000 that are not…

Q: 15. Decide which of these integers is congruent to 6 modulo 19. a) -32 b) 63 c) -49 d) -11 e) 38

A: Here we have to find which integers are congruent to 6 modulo 19. For this Let us understand a…

Q: How many three numbers with no repeated digits, can be formed by the use of the digits 0, 2, 3, 4,…

A: here AS PER GUIDELINES I HAVE CALCULATED 3 SUBPARTS  Three digit number is formed using digit…

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.