A = {R, O, G, E} a) . S={ all words that can be made from letters in A that are shorter than 6 letters}. Calculate the cardinality of S? b) M={ all finite words that can be made from letters in A }. What is the cardinality of M? Justify. Explain it correctly both subparts.

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: Calculate the cardinal number of the set Q containing all the digits that make up the number Q=…

A: The number of distinct elements in a finite set is called its cardinal number or cardinality of a…

Q: Give the cardinality of each set. M:(1st 5 multiples of 5)

A: Given that we need to find cardinality of a set M:{first 5 multiple of 5} Since first 5 multiples of…

Q: Suppose we modify the construction of the Cantor set by starting with the open interval (0, 1) and…

A: The interval is (0,1) To construct Cantor's set.

Q: What is the best choice for the cardinality of the set of all finite subsets of N (N = { 0, 1, 2,…

A: Concept : The cardinality of the set is the measure of the no. of elements in the set . for, finite…

Q: Prove that the set of irrational numbers has the cardinality of R.

A: In informal terms, the cardinality of a set is the number of elements in that set. If one wishes to…

Q: Show that the two given sets have equal cardinality by describing a bijection from one to the other.…

A: According to the given information, it is required to show that the two given sets have equal…

Q: Give the cardinality of the set. (If the set has cardinality 80, enter ALEPH NULL.) {44, 45, ...,…

A: To determine the cardinality of the given set.44, 45, ..., 169, 170

Q: Suppose set A = {green, blue, red, black, orange} and set B = {gray, purple, blue, orange, white}…

A:

Q: Investigate and illustrate the cardinality of the sets of odd numbers, ?, and ℤ, which properly…

A:

Q: (a) Suppose that we choose three subsets of M such that each of them con- tains 100 elements, the…

A: Let the three subsets be A, B and C  nA∪B∪C=nA+nB+nC-nA∩B-nB∩C-nA∩C+nA∩B∩C Substitute the values…

Q: Using roster method, list down the elements of the given sets below and determine its cardinality 1.…

A: 1. G= set of all odd nnimbers between 11 and 23

Q: If a set B has 64 proper subsets of odd cardinality, what is |B|? O 6 O 7 O 8 O 9

A:

Q: Calculate the cardinal number of the set Q containing all digits that make up the number q=…

A:

Q: What proof techniques are used to show that the cardinality of the power set of a finite set S is 27…

A:

Q: What is the best choice for the cardinality of the set of integer values in [0,10]   finite…

A: in given interval possible integers are 0,1,2,3,4,5,6,7,8,9,10, which is finite

Q: A survey of 104 college students was taken to determine the musical styles they liked. Of​ those, 35…

A:

Q: A survey of 128 college students was taken to determine the musical styles they liked. Of​ those, 50…

A: Solve for venn diagram

Q: In the set of {1,2,3,4,5,6} can we use the formula 2^n (n stand for how many even number inside the…

A: This is a problem of set theory.

Q: Let a be a cardinal number >1, and let b be an infinite cardinal numb er. Prove that if a = ab, then…

A: Given: a is a cardinal number greater than 1 Also, a=ab ⇒a-ab=0⇒a1-b=0 So, either a=0 or 1-b=0 As it…

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

A:

Q: A survey of 105 college students was taken to determine where they got the news about what's going…

A:

Q: We form the union of a set with 5 elements and a set with 9 elements. Which of the following numbers…

A:

Q: Find the cardinality of each of the following sets.  ? = {2, 5} ? = {3, 4, 5, 6, 7, . . ., 31} ? =…

A: The cardinality of set: The cardinality of a set is the number of elements in the set. An element of…

Q: If a is an infnite cardinal number and a ⩽ bc, prove that a ⩽ b or a ⩽ c

A: Image is attached with detailed.

Q: What is the cardinal number of the set E if it comprise of the letter from the word…

A:

Q: A survey of76college students was taken to determine where they got the news about​ what's going on…

A: Topic : venn diagram

Q: so the S and T remain next to each other (though not necessarily in that order, so ST or TS are both…

A: Consider as S and T as one letter. So now the total number of English alphabet which needed to…

Q: Prove that [0,1] has the same cardinal number as [0,2] U[7,9].

A:

Q: Show that the given set has a cardinality of No by establishing a one-to-one correspondence between…

A: Here the function is  f(n) = -6n-6  Consider two points n1, n2,  f(n1) = f(n2) should imply n1 = n2

Q: An infinite cardinal number a is said to be dominant if it satisfies the following condition: if b…

A:

Q: Determine the cardinality of each of the sets, A, B, and C, defined below, and prove the cardinality…

A: (1) The given set  A is the set of irrational numbers. We know that set of real numbers ℝ is an…

Q: Find the cardinality of the following set. B={1,3,5,...,25} n(B)= ?

A:

Q: A survey of 86 college students was taken to determine where they got the news about​ what's going…

A: Given Information: There are 86 college students in total. Of which, 31 got the news from​…

Q: Given A={2,4,6,8} and B={1,3,5,6}. What is the cardinality of the union of set A and B?

A: Number of element in A union B is 7. Actually in sets we are not writing same element in twice.

Q: What is the cardinality of the set of letters in the word “vaccination”

A: Given: "Vaccination" We can write the word "Vaccination" as, S=v,a,c,c,i,n,a,t,i,o,n which is the…

Q: III. Enumerate the elements of the following. Moreover, determine the cardinality of each set. 7.…

A:

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

A:

Q: Find the cardinality of the set(22,44,88,176)

A: The cardinality of a set is the number of elements  in the set. The given set is 22,44,88,176

Q: Find the cardinality of the set A A= (0. (0). (0, (0) }} Multiple Choice 2. as this set contains…

A: The cardinality of a set is the number of elements in a set. Let A be a set. The cardinality of A is…

Q: 5. Prove that if ac < b°, then a <b where a, b, c are car din al numbers.

A:

Q: Give the cardinality of the set. (If the set has cardinality ℵ0, enter ALEPH NULL.) {47, 48, . . .…

A: Cardinality of a set is the number of elements in a set.

Q: A survey of 116 college students was taken to determine where they got the news about what's going…

A:

Q: We form the intersection of two sets. We know that one of them has n elements and the other has m…

A: Given : A=n , B=m To Find : Cardinality of A∩B

Q: III. Enumerate the elements of the following. Moreover, determine the cardinality of each set. 6.…

A:

Q: A survey of 70 college students was taken to determine where they got the news about what's going on…

A: Venn diagram is the graphical representation of a set .Universal set is represented by a rectangle…

Q: 8. The set of even numbers less than 100 is infinite. 9. The cardinality of a null set is zero. 10.…

A: 9. Cardinality of any set is the number of distinct elements that set contains. for example- P=A,B,D…

Q: Given that |A| = 10 and |AUB| = 24 and |ANB|=7, determine the cardinality of B.

A: We are given that : A=10A∪B=24A∩B=7 Now, we have :A∪B=A+B-A∩B⇒24=10+B-7⇒24-10+7=B⇒21=B⇒B=21⇒Number…

Q: (c) X = {Bora Bora, Santorini, Bali, Majorca, Capri} is the set of all five items. (i) How many…

A: One can select m items from n items in nCm ways when order of the items is not considered.  Here we…