Supposing the binary operation * is defined on the set T = {1, 2, 3, 4, 5} by a * b = a +b+ 2ab. Say 2, 3 e T, so 2 *3 is closed under operation *.

Q: Draw the Hasse diagram for the partial ordering {(A, B) / AcB} on the power set P (S) where S…

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Q: (iv) The power set P(C) of C by listing down the elements directly.

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Q: 1. Let H = {1, 2, 3, 4, 5} and the rlation RC H², with (a, b) ER + a = b( mod 3). • Give the set R.…

A: R ={(1, 1), (2, 2), (3, 3), (4, 4), (5, 5)}

Q: Let {0,1}N = {(ao, a1, a2, ...) : an = 0 or 1, n E N}. • Construct a 1-1 correspondence between {0,…

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Q: 6. Prove that if gcd(a , b) = 1, then gcd(a + b, ab) = 1.

A: We need to prove that if gcda,b=1 then gcda+b,ab=1 Let us on the contrary assume that  gcda+b,ab=c…

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Q: 8. Prove the idempotent laws in Table 1 by showing that a) AUA = A. b) ANA= A. %3D 9. Prove the…

A: Let's find.

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A: .

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Q: 7. Let B₁, be the set of bitstrings of length n. Describe a bijection f: P({1,2,...,n}) → B₁.

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Q: السؤال 12 Let T-{1,33. 1 1 1 .}, then T is countably infinite set. 2 in صواب ihi

A: We Know that We say a set X is countably infinite if |X| = |N| where N is set of Natural Numbers.

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Q: Show that gcd (f1,..., fa) = gcd ( f1, gcd (f2, ... , f,)) for any s > 3.

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Q: 5. Construct a smallest binary relation S defined on the set {w,r, y, z} such that S satisfies all…

A: Consider the set, A=w,x,y,z, where all the 4 elements are distinct.

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A: We have to show that any language A is recognizable if and only if A≤mATM.

Q: (a) Let * be defined on Z by a * b = 2ab. Determine whether the binary operator defined is…

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Q: (2) Let R be binary relation on N defined by rRy if and only if r <y< 2r. Is R reflexive? Is R…

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A: Equivalence relation

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Q: m = ∞ Exercise 8.9. Let (91, 92, ..., 9m) € G₁. Prove that |(91, 92, ..., 9m)| = ∞ if and only if…

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Q: Lemma 2.3.7. Let T be a collection of sets with the property that the intersec- tion of any two…

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A: our objective is to prove the result

Q: 1. Which of the following binary relations defined on Z, the set of integers, Is HOI aRb e a is a…

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Q: A is an ordered pair (G,*), where G is a nonempty set and is a binary operation on G.

A: We can solve this as follows:

Q: Let R be the set of all binary relations on the set {1, 2, 3}. Suppose a relation is chosen from R…

A: Introduction :Given , R : set of all binary relations on the set {1,2,3}We have asked to find the…

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Q: Let A1, A2, ..., An be a family of distinct finite sets of positive integers where n = m² +1. Show…

A: let A1 , A2 , ...., An be a family of distinct finite sets of positive integers where n=m2+1. show…

Q: Let A be a set with 10 distinct elements.  i) How many binary relations on A are there? ii) How…

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A: Please check the detailed answer in next step

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Q: 10. Let be the relation defind on Z by „R, if and only if a|b. Orve an explicit description of the…

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Q: Let Σ = {0, 1, +, =} and S = {x = y+z : x,y,z ∈ {0,1}* and x,y,z are binary integers, and x is the…

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Q: Consider z and the binary relation on A given by R=( (x,y)lx+y = 10) For each item, fill the blank…

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Q: Show that there is essentially only one (7, 7, 3, 3, 1) design, as follows. Assume that the elements…

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