23. For each of the following set o (a)Σχ” (b) (ΣΧ) (c)Σ(X- X

Q: contrapositive and converse of each statement. (a) If all birds fly, and if Tweety is a bird, then…

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Q: 1. Let S = {1,2, 3, 4}. (a) How many relations are there on S? (b) How many are reflexive? (o) How m…

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Q: (ii) for every singleton set A, m* (A) = 0.

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Q: (e) If each fn has at most a countable number of discontinuities, then f hasat most a countable…

A: Consider the example: fnx=1q             x= pqwith p,q∈N, gcdp,q=1,q≤n0             otherwise So,…

Q: Let S be the set S={(x+y) l 2x+3y>=(greater than or equal to) 12} What would be Sc  (S complement)…

A: The given set is: S=x,y∈ℝ2 | 2x+3y ≥12 Cleary S⊂ℝ2.

Q: Let P(x) be the statement "x spends more than five hours every weekday in class," where the domain…

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Q: Apply K-map to simplify the following Boolean function to product-of-sums form: (a) F(w, x,y, z) =…

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Q: (e) ((SNT)US) (f) U-S (called the complement of S) Given that the set S contains n elements, show…

A: To show that a set S with n elements has 2^n subsets, you can use the concept of the power set. The…

Q: The notation vxP(x) denotes the universal quantification of P(x). Here v is called the universal…

A: We will find out the required value.

Q: If (f +g) € R[a, b] , then (f.9) € R(a, b] (f - 9) € R[a, b] E R[a, b] none of these

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Q: The Maclaurin series for f(x) = x'e2) ts: -2)*x**2 (b) (a) (e) None kl k!

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Q: A. Use laws of Boolean algebra to simplify the following Boolean expression [(XY') +Y']'

A: Using De Morgan formula and other laws of Boolean algebra: XY'+Y''=XY''Y''…

Q: Let F(x.y): "x is friend with y", N(x): "x is funny", W(x): "x is wise", R(x): "x is fair". The…

A: The symbolic is given as follows: ∃x∀y¬Nx∧Wx∧Ry→¬Fx,y We are given that: Fx,y: "x is friends with…

Q: Let F(x,y): "x is friend with y", N(x): "x is funny", W(x): "x is wise", R(x): "x is fair". The…

A:

Q: The counterexample of A = {1} and B = Ø disproves which of the following statements where P(X)…

A: Given that A=1,B=∅. For (a). PA∩B=P1,∅∩∅=P∅=∅ And, P(A)∩P(B)=P1∩P(∅)=1,∅∩∅=∅ Hence statement of (a)…

Q: Let S be the set of all strings of a's and b's of length 3. Let B = {0, 1}. Let f: S B be defined as…

A: S be the set of all strings of a's and b's of length 3 . Then to find f(aaa) , f(aab) , list all the…

Q: Let A = {1, 2, 3}, B= {4,5,6, 7} If f: A x B → N with f((a, b) = b – a , find the following. a. f…

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Q: ) Let S be the non-empty set containing all a for which f(x): = monotonic for all xe R. Find S. 4a-7…

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Q: Determine if the following statement is True/False: For every f(n), g(n) such that f(n) ∈ O(g(n)),…

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Q: 6. (a) Let sets S = {A, B} × {1, 2, 3} and T = {A, B} × {1, 2, 3, 4} . How many different one %3| to…

A: The total number of elment in set s will be  and total number of element in set T will be

Q: Let X={x=(x1, x2, X3, X4) : Xi E {1,2,3,4,5,6,7,8,9,10,11,12} for i=1,2,3,4 such that x1 < x2 < X3 <…

A: Given:X={x=x1, x2, x3, x4 : xi∈1,2,3,4,5,6,7,8,9,10,11,12for i=1,2,3,4 such that…

Q: 2. Let S = {0, 1, 2, 3, 4} and T = {0, 2, 4). (a) How many ordered pairs are in S × T? T × S? (b)…

A: 12. Given that,                    S=0, 1, 2, 3, 4  &amp; T=0, 2, 4.

Q: Let X ={a,b,c} and let P(X) be the collection of all subsets of X. (3.1) List all the elements in…

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Q: Let P(x) = (x - 1)(x - 2)² (x-3)³. Find the set of r such that x (a) P(x) = 0, (b) P(x) 0.

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Q: let a and m be the integers with gcd(a,m)=1, what is the relation between ord m (a) and ord m (-a)

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Q: (i) If A and B are two sets such that ACB, then m* (A) ≤m* (B).

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Q: the statement "Every student at Lebanese International University is amazing" can be written as

A: Given L(x) :" x is student at Lebanese International University" M(x) :" x is not amazing"

Q: Find n(A) for the following set. A = the set of integers between - 22 and 22

A:

Q: Evaluate the following sums: (i) Σ(k + 1)x*, |x| < 1;

A: ∑k=0∞k+1xk,      x&lt;1 Note: There is three different question, according to the guidelines we are…

Q: Which of the following operations on the set Z has more than one left neutral element and no right…

A: The correct answer is: (e) Such a prescription does not exist.Explanation:We find which operation on…

Q: 5. Let S be the set of all finite strings of a's and b's. . Define f : S → Z as follows: For each…

A: S is the set of all finite strings of a's and b's f:S→ℤ is defined as follows: For each string s in…

Q: 1. Simplify the given Boolean expressions to a minimum number of literals: a. XYZ + X'Y + XYZ'

A: