Each of the 20 students learn exactly two of the three languages: English, French and German. 80% of students learn English and 50% of them French. What percentage of students learn German? Use inclusion-exclusion principle for three sets.

Q: How many unordered selections of three elements can be made from the set {a, b, c, d, e, f}?

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Q: List all of the subsets of (x, y, z).

A: Given that the set x,y,z. Find all the subsets of the given set. Definition: A set is a well-defined…

Q: How many ways are there to choose two subsets A and B of [n] so that A ⊆ B, and |B| is even

A: Using logic of sets and subsets we will solve the problem. Using facts we will find a solution to…

Q: R.4. Verify the Principle of Inclusion-Exclusion for the union of the sets A = {1, 2, 3, 4, 5}, B =…

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Q: Prove that at a party where there are at least two people, there are two people who know the same…

A: There are two cases to consider:   Assume there is a someone at the party, who knows everyone else…

Q: Suppose X is a set with 84 elements that is partitioned into four subsets: X1, X2, X3, and X4. If X1…

A: Given total number of elements = 84 Let  number of elements in X4 be a As X1 has twice as many…

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

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Q: If set Z has 7 elements, how many subsets does it have?

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

A: Given : F = 4, 5, 6, 7, 8

Q: Suppose that we have a shipment of 50 microprocessors of which four are defective. In how many ways…

A: Given: shipment of 50 microprocessors of which four are defectiveTo find that:  In how many ways can…

Q: If X and Y are two sets such that X ∪ Y has 18 elements, X has 8 elements andY has 15 elements ; how…

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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: There are six tutors, four juniors and two seniors, who must be assigned to the 6 hours that a math…

A: Part (a): It is given that there are 6 tutors, four juniors and two seniors. The math center is open…

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

A: The five marbles(none of them are red or green) to be selected from a bag containing 5…

Q: If A and B are both finite sets and A has n elements and B has m elements, what’s the fewest number…

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Q: what are subsets?

A: Let us consider two sets A and B.A is called subset of B if and only if B set have all elements of A…

Q: A box contains two black balls, labeled 1 and 2, and five white balls, labeled 3, 4, 5, 6, and 7.…

A: One person to get the both balls by 2 different ways

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

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Q: If a small monster collector has 20 small monster containment devices; intends to use all of those…

A: The small monster collector has containment devices and will use all of them, while capturing at…

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

A: We have 6 Red marbles2 Green marbles1 transparent marble4 yellow marbles2 orange marblesTotal no of…

Q: Find the number m of ways that a class X with ten students can be partitioned into four teams A1,…

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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: A universal set U with 117 elements has been partitioned into three subsets, A, B, and C. If B is 2…

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Q: How many unordered sets are there of two items chosen from four? sets

A: To Find: How many unordered sets are there of two items chosen from four? Concept: Crn=n!r!n-r!

Q: How many subsets are there of the set N = {5, 42}?

A: We ahave to find no. Of subsets.

Q: rom a group of 7 men and 5 women, how many committees of size 3 are possible.  a) With no…

A: Given: No. of men=7 No. of women=5   Committee members=3

Q: Find the number of ways in which a committee of ilher A or B but not both must be a member of the…

A: Combination is a tool of selecting the n items from the m choices. Always n is smaller than or equal…

Q: If X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and X ∩ Y has 10…

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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: How many subsets are there for the set {h, j}?

A: The given set is {h, j}.It is known that, “If a set contains ‘m’ elements, then the number of…

Q: Assume that you have a total of 11 people on the board: 4 out-of-state seniors, 3 in-state seniors,…

A: Given- Assume that you have a total of 11 people on the board: 4 out-of-state seniors, 3 in-state…

Q: suppose we color the squares of a 4×4 grid blue or red.Using inclusion-exclusion, how many ways can…

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Q: If a set S has n > 3 elements, how many subsets of S have less than n – 1 elements?

A: Apply the simple logic of Permutation & Combination.

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 Find the sets of five marbles containing 2 yellow marbles:…

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: Use the inclusion-exclusion principle: Consider the set of 21 consonants and 5 vowels.  How many…

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

A: Given:  4 Red Marbles 3 Green Marbles 1 Transparent Marbles 4 Yellow Marble 3 Orange Marble  To…

Q: Of all the books at a certain library, if you select one at random, then there is a 90% chance that…

A: Percent: It is the hundred part of the whole It is denoted by '%' The percentage can be written in…

Q: If 1/3 of the blocks in set A are red, and 1/4 of the blocks in set B are red, does it follow that…

A: Given 1/3 of blocks in set A are red and 1/4 of blocks in set B are  red

Q: Assume that you have a total of 9 people on the board: 3 out-of-state seniors, 1 in-state senior, 2…

A: To work out the number of selections under the given conditions

Q: andomly selected from a

A: we have given a sample of 6 measurements was randomly selected from normally distributed population…

Q: How many unordered sets are there of four items chosen from six? sets

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Q: find the subset of (E, B,T,*)

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Q: A box contains 4 black, 2 red and 3 white marbles. In which of the following ways is it correct to…

A: Given: A box contains 4 black, 2 red, and 3 white marbles, and 4 balls are selected from this box. 4…

Q: Show that in a group of people there must be two individuals that have the same number of friends…

A: We make a proof by contradiction and use the pigeonhole principle.

Q: Find the complement of the set.{x∣x is a whole number less than 6} if U is the set of all whole…

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Q: Find the union of the sets {a, e, i, o, u} ∪ ∅

A: Given: The set {a, e, i, o, u} and ∅ function. {a, e, i, o, u} ∪ ∅ To find: The union of the set.

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

A:

Q: Suppose XX is a set with 144 elements that is partitioned into four subsets: X1, X2, X3, and X4. If…

A: To determine the number of elements in each subset in the partition.

Q: A given large basket can contain 70 pieces of fruit consisting of apples, bananas, kiwifruit,…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.