6. In a group of 60 people, 27 prefer cold drinks and 42 prefer hot drinks, with each participant preferring at least one of the two. How do we find the number of individuals who enjoy both coffee and tea? * Let A = Set of people who like cold drinks B = Set of people who like hot drinks

Q: Find a b. a = 61 + , b-1 - 9) + k

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Q: Let A = {Dirk, Johan, Frans, Sarie}, B = {Frans, Sarie, Tina, Klaas, Henrika}, C = {Hans, Frans}.…

A: The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A…

Q: The product of two integers of the form 6k + 5 is of the form a. 6k + 5 b. 6k-3 O c. 7k + 1 O d. 6k…

A: We can give the answer as below

Q: An BnC (A-B)U(A-C)U(3 Match each of the options above to the items below. S Di An (BUC) 4

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Q: Find, if possible, (a) A + B, (b) A − B, (c) 2A, (d) 2A − B,and (e) B + 1/2 A.

A: a). b).

Q: In AABC, DE || BC, find x. x+2 D. 6, E x+1 C 2.

A:

Q: →                      →               a = (−5, 3) and b = (−1, −2), so →   →   a + b = _____?

A: Given: a→=-5,3, b→=-1,-2 We know that sum of two vectorsp→=x1,y1,q→=x2,y2 is given by p→+q→=x1+x2,…

Q: Use the union rule to answer. If n(A) = 9, n(B) = 10 and n(A N B) = 3, what is n(A U B)? ... n(A U…

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Q: Use the union rule to answer. If n(A) = 6, n(B) = 10 and n(A N B) = 4, what is n(A U B)? n(A U B) =

A:

Q: What is the difference of (e+fi)-(g+hi)

A: To find the difference of (e+f i ) -(g + h i )

Q: Decide if the following n can be expressed as the sum of squares. If it is possible then provide…

A: This problem is based on the sum of two squares theorem. We first state the theorem and then give an…

Q: Which example does not illustrate the commutative property? A. 6(x+4)= (x+4)6 B. 2+ (8y + 3x)=2+…

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Q: Use the union rule to answer. If n(A) = 10, n(B) = 15 and n(AB) = 8, what is n(A U B)?

A:

Q: Express the sum of numbers from 5 to x.

A: In this question, we find the sum of the numbers from 5 to x  here we use the formula of the series…

Q: III. Workout (Show all necessary steps). 11. Simplify the following expressions: a. 2V2 (V3+2) C.…

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Q: Find, if possible, (a) AB and (b) BA.

A:

Q: If n(A) = 28, n(B) = 25, n(C) = 24, n(A n B) = 8, n(An C) = 12, n(B n C) = 7, and n(A U BUC) = 55,…

A: To find n(AΠBΠC)

Q: In Z12, what is the order of a +b if a = 6 and a = 2? 3 A C B.

A: SOLUTION-

Q: Find, if possible, (a) AB and (b) BA.

A: (a) Consider the given matrices A and B. As the number of the rows is equal to the number of columns…

Q: (B) = 10 and n(A N B) = 4, what is n(A u

A: n(A U B)=12

Q: Find, if possible, (a) A + B, (b) A − B, (c) 2A, (d) 2A − B,and (e) B + 1/2 A.

A: Consider, Thus,

Q: Use the union rule to answer the question. If n(A n B) = 8, n(A U B) = 34 and n(A) = 32, what is…

A: We know,      n(A U B) = n(A) + n(B) - n(A ∩ B)      => n(B) = n(A U B) + n(A ∩ B) - n(A)

Q: EVALUATION A. Express each item in simplest form. 1. (-6x³y*)³ 2. (5a?xy)(b³y*)³ 12x5y* 3. 3x²y3

A: Property 1: (pq)n=pnqn Property 2: amn=amn Property 3: aman=am+n Property 4: p-k=1pk

Q: b) Find P(A or B) P(A or B) = P(A) + P(B) - P(A and B) = ANSWER E 178 120 + 250 250 e) Translate (b)…

A: Probability is a chance factor, which can occur any outcome of the random experiment.…

Q: Which expression has the smallest value? F19| A |-34| D 47| D.

A:

Q: 37. Which diagram shows (AU B) UC? (A) (В) (C) (D) 38. Which diagram shows (AU C) N B (A), (В) (D) C

A: 37) Draw the diagram for A∪B and C as follows, Draw the diagram for A∪B∪C as follows, Therefore,…

Q: Find (- 3)BA + (6)CD, if possible. 3 - 5 5 4 -5 1 - 3 D= -2 1 - 1 2 2 3 6 9 - 4 1 Select the correct…

A:

Q: 4 = 70, find n.

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Q: -a b Evaluate-2a +4x 2b-4y x с 2b-4y 2c +4% -Y

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Q: 3.) Select the expression NOT equivalent to the other three. A. -8 - 7n + 16n B. 9(n - 8) C.n-8 +8n…

A:

Q: Ex: Let R = {0, a,b,c} + a G a a b ( a 6 2 2 G b C 0 a C b a O a a b b (C b • @ Show that (R, +,-)…

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Q: If n(A U B) = 20, n(A N B) = 3, and n(B) = 13 , what is n(A) ? Your answer

A:

Q: Which equalion represents O8? 2 B O A. (x-3)++ 3 - 4 B. (x+ 3) - (y- 3) = 4

A: Equation of circle

Q: If n(A) = 104, n(A U B) = 141, and n(A n B) = 42, find n(B).

A: