Let A = {1, 3, 5, 8}, B = {3, 5, 7}, and C = {2, 4, 6, 8}. Find:(a) A ∩ B   (b) A ∪ B   (c) B ∩ (A ∪ C)_

Q: Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {1, 3, 5, 7, 9}. Find A′.

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Q: How many subsets are there of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}? How many of these subsets are proper?

A: Let the given set is A, having elements as

Q: Find projvu.u = (−1, 3, 1), v = (4, 0, 5)

A:

Q: Use double set inclusion to prove that dep. PANB) = P(A)n P(B).

A: The problem is related with power set P of sets. Here, we have to show that P A ∩ B = P A ∩ PB using…

Q: How many subsets does the set  F = {4, 5, 6, 7, 8}  have?

A: Given : F = 4, 5, 6, 7, 8

Q: Consider a bag containing four red marbles, two green ones, one transparent one, three yellow ones,…

A: Total number of marbles = 4+2+1+3+3 = 13

Q: Show that A = {2,3,4,5} is a proper subset of B = {2,4,5,6,3}

A: A set X will be called a subset of Y, if each elements of X belongs to the set Y . A set X will be…

Q: Prove the following in axiomatic system. (A- (-B - C),~B}-A-C

A: Laws of inference are very useful in proving mathematical statements. We can build a sequence of…

Q: (b) Every student in a discrete math class is either a computer science or a mathematics major or is…

A: The union of events A and B is defined as n(A ∪ B) = n(A)  + n(B) – n(A ∩ B).

Q: Write down the non-empty proper subset of the set {a,b,c}. Make sure to use correct notation…

A:

Q: The set of elements in (-, 9) or (-, 12) or in both sets is .

A: The sets are (-∞,9) , (-∞,12)

Q: A box contains 15 balls in which seven are green and eight are yellow. If five balls must be drawn…

A: It is given that Number of green balls = 7 Number of yellow balls = 8 Total number of balls = 15…

Q: Consider a bag containing four red marbles, three green ones, one transparent one, three yellow…

A: Given, four red marbles,three green ones, one transparent one, three yellow ones, and three orange…

Q: Find projvu.u = (0, −1, 2), v = (3, 2, 4)

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Q: How many numbers must be selected from the set {2,4,6,8,10,12,14,16,18,20} to guarantee that at…

A: Use the principle of inclusion and exclusion to solve this problem, as in next step.

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: If a set contains 4 elements then its power set will contain?

A: Here  Set Contains 4 Elements So For n elements  It's Number of powerset =(2^n)

Q: The gift wrap desk at a large dept. store offers 5 box sizes, 10 wrapping papers, 7 colors of ribbon…

A: To calculate the total number of options for the customer at the gift wrapping counter

Q: why Ua equals to empty set

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Q: Assume that A={A,B,C} and B={5,4,1,9,6} A code consists of 2 different symbols selected from X…

A: Given: Assuming X={A,B,C} and Y={5,4,1,9,6}. A code consists of 2 different symbols selected from X…

Q: If A (5, 7, 8, 9}, B = {3, 4, 5, 6} and C = {2, 4, 6, 8, 10}; where n is total number of distinct…

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Q: If A=(1,2,3,4,5.6,7), What is the number of nonempty subsets of A?

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Q: List all the subsets of (bear, dog, sheep}. O A. (bear, dog, sheep}, {bear, dog), {bear, sheep},…

A: Given set is {bear,dog,sheep} Now, we need to find all the subsets of given set (i.e) the power set…

Q: Number theory

A:

Q: Assume that there are 6 types of upholstery, 2 types of wood, and 5 designs to choose from. Of the…

A: Of the 5 designs, 4 designs permit both a choice of wood and a choice of upholstery. We can pick…

Q: Let ū = (3, – 4, – 10) and i = (– 7, – 2, 0). – 2,0). - - 2u + 20

A: Given:-u→=<3, -4, -10> andv→=<-7, -2,  0>

Q: Let [A1, A2. [B1, B2, C1, C2 be 3 married couples who attended a concert in Windhoek. a) In how many…

A:

Q: Let ū = (3, – 4, – 10) and i = (– 7, – 2, 0). - 2ü + 20 (-8,-12 - 20)

A: Given :-  u=<3,-4,-10>  v=<-7,-2,0>  To find:-  2u+2v

Q: How many subsets does the set  F = {3, 4, 5, 6, 7} have?

A: No. of subsets in a set: The number of subsets in a set containing n elements is given by 2n. No. of…

Q: Let U = {1,2,3,4,5,6,7,8,9,10} and A = {1,3,5,7,9). Find A". ....

A: Given, U=1,2,3,4,5,6,7,8,9,10   AndA=1,3,5,7,9

Q: Let A {1,3,5, ... }, then A is well- ordered.

A: Here we have given a set A ={1,3,5,  ...}

Q: Suppose you have 6 black and 9 white t-shirts and you dont want to put black ones on top of another…

A: The number of white t-shirts=9 The number of black t-shirts=6

Q: What is (A∪B)c where A={5,11,3,8,9} , B={99,5,11,2,4} and Universal Set…

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Q: A committee of 5 is to be made from 3 students and 6 teachers. In how many ways can this be done a.…

A:

Q: How many subsets of set S = {1, 2, 3, 4, 6} do not contain odd numbers? Use bijection to solve this…

A: Solution S={1,2,3,4,6}

Q: Find projvu.u = (2, 3), v = (0, 4)

A: Given: Let the vector u and vector v be: Formula used:

Q: Is A a subset of B if A = {2, 3, 5, 7, 8, 9, 10} andB = {3, 5, 8, 9}?

A: The given sets are, A=2,3,5,7,8,9,10B=3,5,8,9 A set A can be said to be the subset of another set B…

Q: Find projvu.u = (2, 5), v = (0, 5)

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Q: A carton of 15 light bulbs contains one that is defec-tive. In how many ways can an inspector choose…

A:

Q: A  commitee of 2 teachers is to be formed in a school such that there is one male and one female…

A: We can pick a female teacher from 12 female teachers in 12 ways.  We can pick a male teacher from 15…

Q: How many subsets of a set with 64 elements have more than two elements

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Q: How many subsets is obtained from a set with 5 elements?

A: Given n=5

Q: Let $\quad U=\{1,3,5,7,9,11,13\}, \quad A=\{1,3,5,7,9,11\}, \quad B=\{1,3,7,9\}$,$C=\{3,9,11\},$ and…

A: U=1, 3, 5, 7, 9, 11, 13A=1, 3, 5, 7, 9, 11B=1, 3, 7, 9C=3, 9, 11D=1, 9

Q: How many elements are in the set {0, {0}}?

A:

Q: Set A contains 6 elements, set B contains 12 elements, and 4 elements are common to sets A and B.…

A: Set A contains 6 elements, set B contains 12 elements, and 4 elements are common to sets A and B.…

Q: Prove: 4 x,,x2x, ER, then |x, +x, +.. + x,| s |x,|+|x,|+... + |x,|

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Q: Find projvu.u = (2, 4), v = (1, −5)

A: The projection of u onto v is denoted as projvu. The following formula is used to find projvu.…

Q: How many ways are there to arrange the 26 letters of the alphabet so that no pair of vowels appear…

A: To find number of ways are there to arrange the 26 letters of the alphabet so that no pair of vowels…

Q: 2. Let A = {0, 1, а, b, 8, 10, с, — 4}, В 3D {3, 1, 9, e, а, с, 0}, and С %3D {2, с, 10, 9, 8, —4,…

A: Using the definition of intersection, union and difference between two set

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.