Let A = {a, B} be the set of alphabets and let L be the set of all palindromes over A. Write the recursive definition for L.

Q: Let (A, 3) be a poset, and let BC A. Prove that B has at most one greatest lower bound.

A: Let, A,<~ be a poset and B is a subset of A and a∈A. Then by the definition, a is the greatest…

Q: Let m, n,kEN such that k s min(m, n) Show that (Hint: from a count argument) C₁=CC₁+C₁ C₁+CC

A: Given: Let m, n, k∈ℕ such that k≤minm,n. To show: Ckm+n=C0Cknm+C1Ck-1nm+…+CkC0nm

Q: Let A be a set with |A| = n. Using induction, prove that |P(A)| = 2^n .

A: To show that the cardinality of power set of A is 2n when given that cardinality of A is n.

Q: Prove by induction that for sets A1, A2, . .., An, п п A; =UA. i=1 i=1

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Q: Let N be a set of counting numbers. Which among the quantified statements is TRUE?

A: Explanation: Given that,  N is the set of counting numbers.   Concept Used: Counting numbers are set…

Q: Is (R,#) a poset? If it is a poset, is it a total order? (R is the set of all real numbers)

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Q: Use the pumping lemma to show that the language {www | w E e {a,b}*} is not regular.

A: Consider the provided question, We need to show that the language www|w∈a,b* is not regular by using…

Q: Given the universe of discourse as the set of natural numbers, N, use induction to prove P(n): 2"…

A: Here prove that Pn: 2n>n2 is true ∀n≥m

Q: O Show that if A is finite, then P (A) is finite.

A:

Q: Fix an alphabet. For any string w with |w| > 2, let middle(w) be the string obtained by removing the…

A: Given: L is a regular language on ∑. To prove: The set f1L=ω: middleω∈L is regular for any string ω.…

Q: (c) Prove that if A and B are finite sets, then A B is finite and A B| = |B|Al. (Hint: Use induction…

A: For (c), We are given that if A and B are finite sets. So, let |A| = m and |B| = n. Now, we need to…

Q: Write the following set in roster form: A={x:x is any two elements that belong to natural number…

A: Just observe step by step, we'll see a pattern.

Q: .Suppose A is an open set in R. Show that the set B= An(-10, 10| is compact, where R is the set of…

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Q: Prove that, there is no simple grcup of order 200.

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Q: Let A (k,s), t.en the power set of A is:

A: Set of all subsets of A is called power set of A.

Q: Suppose a set A is uncountably infinite, that U is countably infinite, and that UC A. Show that A -…

A:

Q: Let (Un) be a sequence of open sets in R then a) U₁is open, b) nis open.

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Q: Cantor set is uncountable .A O

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Q: Prove by induction that for sets A1, A2, . .,An, n A¡ i=1

A: For induction method we take a statement. We will show that the statement is true for n=1, n=2 then…

Q: the set of students at your school who either are not sophomores or are not taking discrete…

A: Given: Suppose that A is the set of sophomores at the school and B is the set of students in…

Q: (2) (a) Show using set identities that AUBU (AOBOT) = AUBUT (b) Prove by contradiction that if A C…

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Q: uppose that A ⊆ C so that n(A) = 5 and n(C) = 11. How many subset B, with n(B) = 8 are there such…

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Q: Let f and g be permutations. Show that the order of h=fgf^−1 is the same as the order of g.

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Q: If a language is any set of strings in E*, where E + Ø, prove that the set of all languages is…

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Q: Let s be a string of length 2 with characters from {0, 1, 2}, and define statements a, b, c, and d…

A: Let s be a string of length 2 with characters from {0, 1, 2}, and define statements a, b, c, and d…

Q: 1. Show that if A is a subset of B, then the power set of A is a subset of the power set of B.

A: Hello, thanks for your question but according to our policy, I am answering the very first question.…

Q: Let P be the set of all positive factors of 90, and let / denote the 'divides' relation. Then the…

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Q: Let =P(N), then & is Boolean algebra. ulgn

A: True Statement

Q: is the number of ways of selecting from a set when the order is not important. a. Circular…

A: The number of ways selecting from a set when order is not important is called Combination.     Note:…

Q: In the given questions,suppose m and n are positive integers, A is a set with exactly m elements,and…

A: Given: m and n are the positive integers. Set A contains m elements and set B contains n elements.…

Q: 106. Let a e Z, and let M, be the smallest inductive set containing a. Then Ma = Zza.

A:

Q: Let x be  a set containing 20 elements. Use the multiplication princple to compute |p(x)|, the size…

A: It is given that, the number of elements in the set X has 20.The power set P(X) of a set X is the…

Q: Since by definition a language L over an alphabet A is just a subset of A*, the set of all languages…

A: If no condition of a language is given, then the above statement is true and the reasoning for the…

Q: Write an element from the set B × A × C

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Q: Let S be the set of all strings in a's and b's, and define C: S → S by C(s) = as, for each s ∈ S.…

A: Let S be the set of all strings in a's and b's. Given that, C:S→S, defined by Cs=as, ∀s∈S To show…

Q: Use the element method and contradiction to prove that for all sets A, B, and C, if A C then An…

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Q: Let S be the set of all strings of O's and 1's of length 4, and let A and B be the following subsets…

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Q: Let 9= {[a,b]: a,bER}, then 9 is Borel algebra

A: TRUE ;

Q: Consider the usual order R on the set A of lower case English alphabet letters. Then the…

A: Given:  Under usual order R on the set A of all lower casesin English alphabets…

Q: In the given questions,suppose m and n are positive integers, A is a set with exactly m elements,and…

A: Given that,                     m and n are positive integers.                    A is a set with…

Q: Define the sets D = In E N} n+1 Prove whether D is finite, countable, or uncountable?

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Q: Consider the pantial order L on the Ael A =h Luffy, Zoro , Sanji, Chopper, Robin, Brook, Nami, Usopp…

A: Total Order Relation:- Let  R be a relation on a set say X then R is Total Order Relation on X if 1.…

Q: Prove. Suppose that L and M are regular languages on a set A. Then L ∩ M is also regular.

A: Let us suppose L  is regular Language  then L=L(R)  Regular language is closed under certain…

Q: Let A = {a,b, c} and B = {b, c, a}. Prove that A = B. Thus, the order %3| in which the elements are…

A: The given sets are A={a,b,c} and B={b,c,a}we have to show that A=BResult : two sets A and B are…

Q: Let R be the divisibility relation (|) on A = {3,5, 6,7, 10, 20, 30}. We know that (A, |) is a…

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Q: Each character in a password is either a digit [0-9] or lowercase letter [a-z]. How many valid…

A: Each character in the password is either a digit or the lower case letter. considering there is no…

Q: Let B be a finite set and (E

A: Given- A finite set B.          -A a Boolean AlgebraB,*,+,,0,1with respective boolean To Prove - The…

Q: For any set AcR, A is a Borel set.

A: Hi! As per norms, we will be answering the first question. IF you need an answer to others then…

Q: Which of the sets S over {a,b,c} below is defined by the following recursive definition? Base: empty…

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…