Let A and B be finite sets with |A| = m and |B| = n. a) How many functions are there from A to B? b) Suppose that m < n. How many injective functions are there from A to B? How about if m > n? c) Suppose n = 2. How many surjective functions are there from A to B? d) (Harder) Suppose n = 3. How many surjective functions are there from A to B?

Q: 3.Determine the intersection X ∩ Y. Express the  in interval notation. X = {x/ x>equal 8} and Y =…

A: We have: X=x  x≥8=[8,∞)Y=x  x&lt;7=(-∞,7)

Q: write as interval the set defined on the real line 45 67 8 -3 -2 -1 0 1 2 a) b) -2 c) -5 -4 -3 -2 -1…

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Q: Let the universal set R, the set of real numbers. Let A = {x = R | 1 ≤ x6} {x = R | x 6} {x ER 1≤ x…

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

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Q: 4 State whether the following functions are injective and/or surjective. Let R* denote the…

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A: GivenR1=a,b∈R2 , a&gt;bR2=a,b∈R2,  a≥ba) we know that R1+R2 contains thoseelements which are either…

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Q: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: Consider the family of sets F = {Ap}peP, where P denotes the set of prime numbers, and Ap= {p" |…

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Q: need help

A: The objective of the question is to find the set of numbers x that satisfy the condition |8x − 4| ≤…

Q: Eng. analysik By:- ATheer Sale h hect.No.7 Exercises finad favier sexies for the fellouling function…

A: Since you have asked for a multiple question, we will solve the first question for you. If you want…

Q: Identify which sets are equal A = {0,1,2} B = {x ∈ R | -1 ≤ x < 3} C = {x ∈ R | -1 < x < 3} D =…

A: We identify which sets are equal.

Q: For each set of real numbers below: A = {5":ne Z} 2 B = n² 4n²-1 ER} TER n=1,2,...} 22-3, -2,-1, 0,…

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Q: Consider the universal set R, define the interval A = [-7, 1], interval B = (-1,2), and C be the…

A: To solve using interval notation

Q: Let the universal set be the set R of all real numbers and let A={xe R|-2<x<2} and B= {x e IR |-3<x…

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Q: х+ 10 if 0 6 f(x) =

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Q: F and H are sets of real numbers defined as follows. F={y|y21} H= {y |y>7} Write FUH and FnHusing…

A: A set is a well-defined collection of objects. The objects, which belong to the set, are called…

Q: Let the universal set R, the set of real numbers. Let A= {x = R| 1≤x6 } {xЄR|x6} O {x ER 1≤x≤6} ○…

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Q: Determine the union X ∪ Y. Express them in interval notation. X = {x/x>-17 } and Y = {x/x<equal-10…

A: The union of two sets A and B is defined as the set of all the elements which lie in set A and set B…

Q: The maximal interval?

A: Given D.E is    with initial condition   .And solution is

Q: Let A = (x = R: 7 ≤x < 20} and B = {7, 18, 19, 20, 21). What is A - B? A. {x ER: (7<x< 18) (18 < x…

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Q: Q15A. Define the sets A, B, C, and D as follows: A = {y EZ:2 < y ≤ 9 and y is odd}. B = {1, 4, 6} C…

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Q: Determine the intersection X ∩ Y. Express the in interval notation. X = {x/ x>equal 8} and Y =…

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Q: If X, Y are finite sets with |X|=4>2= |Y. How many surjective functions f: X→ Y are there? 2 16 8 O…

A: Let us solve above problem

Q: Consider the universal set R, define the interval A = [-7, 1], interval B = (-1,2), and C be the…

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Q: Let A={1,2,3,5,9}, B={0,6,7,8,10}. Determine (A∖B)∪(B∖A)

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Which of the following defines the domain of |4x-8<12? A) -8<x<-4 B)-4 <x < 8 C) -1<x< 5 D) 1<x<5

A: We can solve the inequality in order to get the solution.

Q: A = {y EZ:2 < y ≤ 9 and y is odd}. B = {1, 4, 6} C = {yEZ: y ≤ 10 and y is even}. D = {y EZ: y ≤ 7…

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Q: Q1: give another description of the following sets 1. {x: x is an integer, 15< x < 25} 2. all the…

A: 1. The provided set is: {x:x is an integer, 15≤x≤25}. The given form is set builder form, another…