1. Let A = (0, 2, 4, 6, 8), B = (0, 1, 2, 3, 4) and C = (0, 3, 6, 9). What are a. AUBUC and b. AnBn C?

Q: 5. Let u = {1, 2,3, 4, 5, , 15} A = { 1, 2, 3, 4, 5 } B = { 1, 3, 5, 7, , 15 } .. Find (An B' )'

A: Given that,

Q: 15. Let A = -8-2-9 4 0 6 4 8 and w= H 21 Determine if w is in col A. Is w€ nul A?

A:

Q: There is a large group of 50 girls. This year 3 of the girls go to study abroad. After the 3 girls…

A: This question is related to permutation and combinations, We will solve it using given information.

Q: Let S = {0, 1, 5, 4, 7}, number of subsets of S is 32Q, then find the value of Q.

A: S is a set with cardinality 5 and given he number of subsets of S is 32Q, then we have to find the…

Q: = [a b] and B =[2³]. a. Compute AB. b. If AB = 1-5₂ 1. Let A = find the entries of A, i.e. find the…

A:

Q: Answer the three parts A,B,C of the permutations and combinations chapter questions with their…

A: We know that number of subset of a set containing n elements is 2n. Also, nCr = n!r!n-r!

Q: Suppose A = {a,b,c,d,e} , B = {d,e,f} and C = {1,2,3}   a) A ∪ B

A: A union  B involves all the elements of A and B once

Q: If a(3, 4) – b(2, 4) = (8, 10), determine a and b.

A:

Q: 0-2 1 -2 0 0 0 duced echelon form of the augmented matrix [A b] i 1 (a) Express the general solution…

A:

Q: 4. Consider A={m,a,t,h}; C={x:x=3n,1šns4,neN}; B={s,t,e,m} ; D={x:x=2n,15n 56,nEN} What is CUD? *

A: Here given that                         A={m, a, t, h}                         C={x:x=3n, 1≤n≤4,…

Q: 1. Let D4₁: = {Po. P1, P2, P3, M1, M2, 81, 82} defined by the following: HIE 2 3 4 234 1234 2 1 4 3,…

A:

Q: If P={a,d,e} , and R={ t,b,c} what is PUR

A:

Q: 2. Given : A= 1 20 A) -10 B) C) D) % 3 Lo -2J -20 -8 -10 8 10 -6 -6 4 [-20 -8 181 20 1 -6 -12 -2 6…

A:

Q: Convert ff Incxag) dA.aver. the.regian.cx.<e. segian.e.x+y.c.e. -.to.polar.form. and.…

A:

Q: {1, 2, 3, 4, ...} is equivalent to {10, 20, 30, 40,.

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

Q: Let A, = {..., – 2, – 1,0,1,..., i}. Find ỦA, i31

A: First we find A1, A2, A3,...An, then find union as in next step.

Q: 1. Give definitions for N, Z, Q, R\Q, and R.

A:

Q: If A={1,2,4} and B={1,3,6}, U={1,2,3,4,5,6}, what is An (AUB) a. {5} b. { } c. {1,2} d. {6} O a Ob…

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Q: 5. Given R ={(1,1), (1, 3), (2, 1), (2,2), (2, 3), (3, 1)} on {1,2,3,4}. Thus, R is reflexive. A.…

A: Given problem :- Given R = {(1,1), (1, 3), (2, 1), (2,2), (2, 3), (3, 1)) on {1,2,3,4). Thus, R is…

Q: If A= {1,2,3,4,5,6,7,8}    B= {1,2,3,4,5}    C= {7,8,9,10}    U= {1,2,3,4,5,6,7,8,9,10} What is B’…

A: Universal set: The set containing all the elements of the related set without the repetition of…

Q: 1. If ü= (2,-3), v=(1, -5), and w=(6, 2), determine the following: a) |ü +v| b) 3 ỹ -ū +w

A: a) u→+v→=(2,-3)+(1,-5)=2+1,-3-5=3,-8=32+(-8)2=9+64=73|u→+v→|=73

Q: If A+B=X and A-B=Y then...?

A: System of linear equations,

Q: Let S = {Ann, Dan, Fran, Jim, Joe, Kim}, A = {Jim, Joe, Kim}, B = {Ann, Dan, Fran}, and C = {Dan,…

A: We have given that  Sample space S = {Ann, Dan, Fran, Jim, Joe, Kim} A = {Jim, Joe, Kim} B = {Ann,…

Q: It is known that there are 20 students, 1 soccer team will be formed. If there are 3 students who…

A:

Q: 4. Define = {1,2,3,4,5,6} and A₁ = {i} for i = 1,2, ...,6, B = {1,4}, C = {2,3,4}, D = {1,2,3} and E…

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Q: 2. If I'faclde- and S'fordx.

A:

Q: 5- 2 Let Ax) =x² + 3r + 5 . and 1 1 2 A = -2 3 3 -1 Which one is f(A)=? 13 11 -10 7 -4 3 12 9. 13 11…

A: We have to find f(A).

Q: 1.3 4) How many different ID cards can be made if there are six digits on a card and no digit may be…

A: GivenNo. of digits from 0-9=10No.of digits to be in ID cards = 6

Q: 6. Given i [2, – 5Jand i [- 7,2] find C.

A: Given v→=[-7,2]We know that magnitude of vector [a,b] is a2+b2

Q: 4. Let A

A: Given,                A=1, 2, a, b, ϕ

Q: 12. If an+2 = 5an+1 O 2268 O 4014 O 2443 O 3129 5an+1 - 6an and ao = 3, a₁ = 7, then a7 =

A:

Q: 4. Let M = {Civic, Corolla, Altima} and S = {Coupe, Sedan} List the elements of M x S.

A: Let M=Civic, Corolla, Altima and S=Coupe, Sedan

Q: 6. 7. With U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15), A = (2, 5, 7, 11, 13), B = $1,…

A: Method: By Using the intersection and union of the events to find the probability

Q: Match the sequence with its graph. 11 1" Select one:

A:

Q: 23. Let A = in Nul A? -6 12 318] and w = [2] -3 6 Determine if w is in Col A. Is w

A:

Q: 1. If P(A) = 0.4, P(B) = 0.5 and P(AB) = 0.3, find a) P(AB) and b) P(AUB).

A: It is given that P(A) = 0.4, P(B) = 0.5, P(A ∩ B) = 0.3

Q: 1. Let, a, = 3, a, = 4 and for n2 3, a,= 2a,-1+ an-2, express a, in terms of n. 2. Let, a, = 3, a, =…

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Q: 2. 3. 3 Let A = {c, d, f, g}, B = {f, j}, and C = {d, g}. Answer each of the following questions.…

A: As Per Bartleby Answering Guidelines We Solve Only One Problem Solution - 2  : Given that the sets…

Q: 1) UA 7-1 | Let A = (0, 1, 2, 3,..., for i = 1,2,3,.... Find 2) ۸ hal

A: Given ,   Ai =  0 ,1 ,2 ,3 ,.......i  for i= 1,2,3...... Then find  1  ∪i=1nAi     2    ∩i=1nAi

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.