1. Let S = {1,2, 3, 4, 5, 6}. Find the following. a. Number of subsets of S of cardinality 5 and having {2, 3, 5} as a subset. b. Number of subsets of S of cardinality 5 containing at least one odd number.

Q: How many subsets of the set {1,2,3,4,5,6,7,8} have cardinality 3 or less?

A: Here we need to find how many subsets of the set A={1, 2,3,4,5,6,7,8} have cardinality 3 or less so…

Q: Find the cardinality of the following set. B = {4, 8, 12, 16, 20, 24, 28, 32}

A: Definition: Cardinality of a set: If a set has finite numbers of elements then cardinality of a set…

Q: The cardinality of { Ø, 1, 2, 2, {1, 2}} is

A: We need to find the cardinality of { ϕ, 1,2,2,{1,2}}.

Q: How many derangements has the set. S? How many derangements of S have 9 in the 2nd position and 1 in…

A: Given, Set S:1,2,.....9 Derangement is a permutation of the elements of a set, such that no element…

Q: Suppose a set of students’ information is formed as S={Student name, ID, contact number,…

A:

Q: 2. a. List all 3-combinations for the set {x1, x2, x3, X4, Xs}. Deduce the value of (,). b. List all…

A:

Q: 1. A₁-[0,4], A2-[1,5), A3= [0.5,3], A4- (1,9] As 2. A₁-[0,4], A₂-[1,5), A3- [0.5,3], A- (1,9] As 3.…

A: Given- Ω=set of all real numbers  A= index set  To identify the generalized union and intersection…

Q: Do A = {1,2,3, 4,...} and B = {-1,0,1,2, 3, 4, ...}have the same cardinality? O No because elements…

A:

Q: Let A= {1,2,3,4,5,6} and B={2,4,6,8}. what is the cardinality of A ∩ b?

A: Cardinality of a intersection

Q: How many subsets of {0,1,...,10} have cardinality 1 or more?

A: Let  We have to find the number of subsets of that have cardinality 1 or more.We know thatIf A is…

Q: 5. For each pair of sets, give an explicit bijection from one to the other, showing that they have…

A:

Q: Let A = {1, 2, 3, 4, ..., 20}. What is the cardinality of the power set of A, P(A)?   Fill in the…

A: Cardinality of Set --: The Cardinality of a set is the total number of unique elements in the set.…

Q: List the first four elements in order of the set { x | x = 4k + 1, and k is a natural number} (List…

A:

Q: Let S={1,2,3,4,5,6,7,8,9} How many subsets of cardinality 6 have {2,3,5} as a subset?

A:

Q: If A={4,5,6}, find its power set P(A). What is the cardinality of this power set?

A:

Q: (a). Show that (0, 1) × (0, 1) and (0, 1) have the same cardinality. (Hint: shuffling two digit…

A:

Q: Show that the N and the set {1,3,7, 15, 31, . . } have the same cardinalit

A: To show N and the set S= {1,3,7,15,31...} have the same cardinality, we need to show there is a…

Q: Show that the following pair of sets have the same cardinality. A = (5, 9] and B = (1, 2) ∪[4, 7]

A: Two sets A and B have the same cardinality provided there is a bijection from A to B.

Q: Find the Car D={a, b, c, d, ..., z), n(D)=? U=universal set n(U')=? B={p people in the USA | p is a…

A:

Q: 2. Let A = {1, 2, 3, 4, 5, 6} and B= {2, 4, 6, 8}. What is the cardinality of B? A U B, A N B?

A: Given that  A={1, 2,3,4,5,6} and B={2, 4,6,8}

Q: How many subsets of {0, 1, ..., 8} have cardinality 6 or more?

A:

Q: How

A:

Q: how many subsets of {0,1 ....,9} have cardinality 4 or more?

A:

Q: Let S={1,2,3,4,5,6} How many subsets are there of cardinality 4?

A:

Q: How many subsets of {0,1,…,9} have cardinality 3 or more?

A: Given set is {0,1,...,9} and we have to find the number of subsets with cardinality 3 or more.

Q: Let A = {1, 2, 3, 4, 5}, B = {8, 9, 10}, and C = {4, 6, 8, 10}. b. What is the cardinality of the…

A: Given: Let A=1,2,3,4,5, B=8,9,10, and C=4,6,8,10. To find: b) Cardinality of the power set of B, PB.…

Q: How many subsets of {0,1,…,9} have cardinality 5 or more?

A: