Q1(a): Let A = {1,2, 3} be a given set. Determine • the cardinality of A the power set P(A) the cardinality of P(A) (b) Find the sets A and B if A – B = {1,5, 7, 8}, B – A = {2, 10}, and ANB= {3,6,9}.

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: 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: Use the set definitions A = {a,b} and B = {b,c} to express the elements of the power set P(A ∩ B)…

A: We Know that A Power set is set of all subsets, empty set and the original set itself.It is denoted…

Q: State the cardinality of the set. The set of subsets of {1, 5, 7, 11, 13}

A: We have to find the number of cardinality of the set.

Q: (4) Q= {all rational numbers}. Cardinality = finite infinite denumerable countable uncountable (5)…

A: Remark: The number of elements in a set S is called the cardinality of S.

Q: Prove that the interval (0, 1) has cardinality aleph-one.

A:

Q: The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of the…

A: From the Venn diagram n(A∩B∩C)=8+3=11

Q: Let B be a denumerable set and let A be a non-empty set of unspecified cardinality. If f : A --> B…

A:

Q: Use the numerals representing cardinalities in the Venn diagram shown to give the cardinality of…

A:

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

A:

Q: Write each of the following sets by listing its elements between braces and then find its…

A:

Q: Consider the set of lattice paths from (0, 0) to (8, 8). You should know one quick formula for the…

A: Using formula,nk=n!n-k! k!i 80=8!8-0! 0!=8!8!=1ii 71=7!7-1! 1!=7×6!6!=7iii 62=6!6-2! 2!=6×5×4!4!…

Q: For each of the following sets, decide whether it is finite, countable, or uncountable. Explain your…

A: Let  be any set , then

Q: Graph the set {x -3<x<2} on the number line. Then, write the set using interval notation.

A: Given, Graph the set {x|-3≤x≤2}

Q: (1 point) Suppose that {A, B, C'} is a partition of the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, where A…

A:

Q: A 8 C 9 n (An Bc) = [ 8 3 5 6 13 B 8 9

A:

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

A:

Q: Prove that each of the following pairs of sets have the same cardinality. (a) We have the sets X and…

A: In set theory, one important concept is that of cardinality, which is the measure of the "size" of a…

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: Let A = {7, 11, 29, 54, 72, 83). Find the set denoted by {[]: € A}.

A:

Q: The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of the…

A: