Let S be a set with exactly n many elements. Arguing by induction, show that the power set P(S) has exactly 2n many elements

Q: a student visits an arcade each day after school and plays one game of either laser man, millipede,…

A: Solution:

Q: An ice cream shop provides the following types of add-ons: hot fudge, caramel, cherry, Reddi-whip,…

A: Consider the  add-ons ice-cream shop provides: Hot fudge,caramel,cherry,redid-whip,chopped…

Q: Select the set that is equivalent to (Cn B) UA. (Cn B)UA (CUB) UA (CnB) nA (CUB) NA

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Q: bag contains three red marbles, one green one, one lavender one, three yellows, and two orange…

A: given data, a beg contains3- red marbles 1- green 1- lovender3- yellows2- orange 10- total marbles

Q: Suppose set A={1,2,3,...,50} is divided into exactly two disjoint, nonempty sets. For example, one…

A: My approach is the I break into 2 disjoint part and take cardinality(number of element) of every…

Q: The binary operation * is defined on the set of R by a * b = (a + b) / (a – b). What is a * b if a =…

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Q: A combination of 3 balls are picked at random from a box containing 5 green, 4 white, and 3 black…

A: Hope this is useful.Thankyou

Q: Let W = {[ W is not 2a 46 : a, b ER ». Determine whether W is a subspace of R³. a subspace of R³…

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Q: Write all permutation for ABC. (Consider as a letter A, B,C).

A: By group theory concepts we have 6 such types of permutations

Q: Let ?={1,2,3,4,5,6}. How many subsets of ?A contain an even number of elements? (How would you…

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Q: Let A be a set with 5 elements and B be a set with 8 elements.  How many elements are in A x B?

A: Given that A be a set with 5 elements and B be a set with 8 elements.  Here we have to find out how…

Q: A universal set U with 66 elements has been partitioned into three subsets, A, B, and C. If B is 2…

A: We use the definition of the size of a set to find the number of elements in the set B. The size of…

Q: A set A has 7 elements. Is it a powerset of another set? That is, is there a set B such that A = 2B?…

A: A set A has 7 elements. It cannot be a power set of another set. Since the cardinality of the power…

Q: Let A = {0, 1,6, 8, 13} and B = {1, 6, 13}. How many sets C have the property that CCA and BCC.

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Q: Let A = {a, b, c, d}. Find the number of 3-combinations of A where repetition of symbols is allowed.

A: We have to count the number of 3-combinations with repetition allowed, we can use the concept of…

Q: 1. Let n E N. Prove the following is true,

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Q: Find the number of 5-permutations of a set with nine elements. use the following formula

A: Number of 5 permutations with nine elements is P(9,5)

Q: Find the complement of the set given that U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. (Enter your…

A: First we find the roster form of the set: The set of odd natural numbers less than 10 = { 1,3,5,7,9}…

Q: 2. Write out the power set of the following set: {1, 2, 3, 4).

A: Solution(2)- Write out the power set of the following set say S={1,2,3,4}

Q: Suppose you have a set S= {1, 2, 3, 4}. How many ways can you arrange 2 elements of the set without…

A: Given   A problem on permutations. Please find the below attachment for clear explanation.

Q: I am given the question  Suppose A = {a, b, c} Indicate which statements below are TRUE.

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Q: Let A = {1,2,{{1,2}}}. Find the power set P(A)

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Q: Let T = {1, 2, 3, 4, 5, 6, 7, 8, 9}. If five integers are chosen from T, must there be two integers…

A: Concept used: The Pigeonhole principle states that if k+1 objects are to distributed in k boxes then…

Q: Let A = {5,6, 7}. What is P(A)? Do not merely describe the set, but rather write down all the…

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Q: Consider the set {1,2,3}. i. Write the elements of the permutations by taking two digits from above…

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Q: Consider the set ? = {3,7,11,15,19, ... ,95,99,103}. At least how many elements must be selected…

A: In the given question we have to find the lest number of the element of the given set s.t there will…