2. Suppose N= {1,2,3...} is the universal set and A = {n :ns7} B = {n : 3s ns 10} %3D C = {2,4,6,8,10} D = {2,3,5,7,8} Find (i) (4©B)U(B®C) (ii) (4®C)U(B®D) (iii) BN(4®D)(iv) (ANB)®(AND) 3. Prove that a = b(mod7)is an equivalence relation by taking suitable examples. 4. Let p and q be positive integers and suppose F is defined as follows F(p.q)={" p< q\ F(p-q)+1_p2q find (i) F(2,5) (ii) F(12,5) (iii) What is work of F (iv) F(5861,7)

Q: What are the possible number of Boolean functions with n-ternary variable?

A: We have to state the possible number of boolean functions with n-ternary variables.

Q: 2. For each of the following relations on the set {1,3,4, 7}. • R1 = {(7, 7), (1, 1), (4, 4), (3,…

A:

Q: 1. Let S = {1,2, 3, 4}. (a) How many relations are there on S? (b) How many are reflexive? (o) How m…

A:

Q: For two sets A and B, if A=B, then (i) A and B have the same elements (ii) ACB and BCA (iii) x €…

A: Here we have to find the properties of two sets A and B is A= B.

Q: 6. Order of operations Evaluate. a) 5(4) + (-1)³(3)² (10-2)²(103)² b) c) (10-2)²(10 - 3)² 6(6 − 1)(6…

A:

Q: . How many Boolean functions are there of degree 7? Explain.

A:

Q: (2) Is the set {r € Rr² € N} countable? Justify your answer.

A: Yes the set A={x €R : x2 €N } is countable

Q: Why does the fact that the orders of the elements of A4 are 1, 2, and3 imply that |Z(A4)| = 1?

A: Given: The orders of the elements of A4 are 1, 2, and 3.We need to signify the given fact to imply…

Q: (e) ((SNT)US) (f) U-S (called the complement of S) Given that the set S contains n elements, show…

A: To show that a set S with n elements has 2^n subsets, you can use the concept of the power set. The…

Q: Let S1= {1, 5, 10, 15, 20} and let S2 = {1, 2, 3, 4, 5}. What is: (a) S1 ∪ S2 (b) S1 ∩ S2 (c) S1 –…

A: Given: The given sets are S1=1, 5, 10, 15, 20 and S2=1, 2, 3, 4, 5. To find: The main aim is to find…

Q: U = {9, 7, 8, 12, 5, 17, 4, 19} A = {9, 4, 19} C = {7, 8, 12, 5, 17} %3D Find AUC' (17, 4, 19) {9,…

A: To Find: A ∪ C'

Q: (b) A committee of 10 people is to be chosen from a group of 12 men and 8 women. How many committees…

A:

Q: Uist all subsets of the set C-(1, 2, 3).

A:

Q: . The sets A, B, C are given by A = {0, 1,2}, B = {a,b) and C= {b,c,d). (a) Find A x B. (b) Find (A…

A: A=0,1,2B=a,bC=b,c,d Remember : A×B=a,b|a∈A, b∈B

Q: (e) Given the sets A = {-5, –3,0, 1, 5} and B = {-4, –3,0, 1, 5, 6}. Find AN B. (A) {-5, –4, –3, 0,…

A: We have to find out the intersection part

Q: You have one pile of 12 building blocks, each one a different color, and you also have another pile…

A:

Q: 8. Show that the set (0, 1) – {1/2, 1/3, 1/4, -..} is uncountable.

A:

Q: You have one pile of 10 building blocks, each one a different color, and you also have another pile…

A:

Q: Find the indicated sets. (a) P({1,2} × {3}). (b) P({1,2}) × P({3}). (c) {X e P({1,2,3}) : 2 EX}.

A:

Q: a) How many derangements ) How many derangements has the set S? of S have 9 in the 2nd position and…

A: Given, Set S:1,2,.....9 Derangement is a permutation of the elements of a set, such that no element…

Q: 1. Let A = {1,2, .., 122}. Determine the number of subsets X CA that satisfy cach condition. In cach…

A: Note: According to bartleby we have to answer only first three subparts please upload the question…

Q: Suppose that you are given n red and n blue water jugs, all of different shapes and sizes. All red…

A: Given:-   red jugs = n blue  jugs = n,    all of different shapes and sizes.  for every red…

Q: A = {−1,0,1,2,3}, B = {12,1,4}, C = {x|0 < x ≤ 2}, D = (−1,1]. Find each of the following sets: 6.…

A:

Q: 1) What is the sum of 8y 1- 2y? and -3y2 + 2y + 7?

A:

Q: Suppose we have a set of n air travellers called p₁,...,Pn. They've just landed at Pearson…

A: Given that:Suppose there is a set of n air travelers called .They've just landed at Pearson…

Q: Acme fastener company makes 6 different types of bolts, and the types are each denoted with a letter…

A: (a) To find the number of different combinations of bolts in each bag, you can use the concept of…

Q: (d) Show that for all integers n > 1 S(n, 1) = 1 = S(n,n), then, using the above relation (or…

A: Given: n≥1 To find Sn,1=1=Sn,n and show that S4,2=7

Q: (7) For any nonzero a, b € Z, the gcd(a, b) divides the lem(a, b). (8) If r, y € Z and 3 divides ry,…

A:

Q: Let S-(0(3).(3.61(3.61).(3.6.9 12) Then the poset (S) is None of these not a total order set because…

A: Total order Set -:  A Poset (A,~) is called total order if any two elements are comparable, i,e. if…

Q: {3*} |리 > 3 z – 3 |리 > 3 z – 3 - |z| > 3 z + 3 - Z |리 > 3 z + 3

A:

Q: 2. Let S = {0, 1, 2, 3, 4} and T = {0, 2, 4). (a) How many ordered pairs are in S × T? T × S? (b)…

A: 12. Given that,                    S=0, 1, 2, 3, 4  &amp; T=0, 2, 4.

Q: 1. For given fuzzy number A={(3/0,4); (4/0,6)(3/0,8)(4/1)}; B={(2/0,7):(3/1): (4/0,7)}. Determine A+…

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

Q: 4. Let A = {a,b), B = {1,2], and C= {1,2,3), and see Definitions 2.2.4 and 2.2.7. (a) List the…

A:

Q: (10) Prove that P(A)n P(B) is equal to P(An B) for any sets A and B. What can we say if the…

A: