Use weak induction to show that if 4, B1, B2 *** Bn are any sets, then Vn 2 2 A U (B1 N B2 N ·.N B») = (A U B1) N (A U B2) N - N (A U B½) ...

Q: 15) n(n*+5) is divisible by for each integer

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Q: P (A) a, P (B) b and P (P (AB)- c then the expression of P (A'B')in erms of a, b and c is:

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Q: What is the output of the circuit corresponding to the Boolean expression (PAQ) V (~Q v R) when: P =…

A: See the detailed solution below.

Q: Given a positive integer n, let a2,n–1 a2,n a3,n-2 a3,n-1 a3,n An = аn-1,2 аn-1,n-2 аn-1,п-1 @n-1,п…

A: Given: Here the given positive integer n, Let An = 00...00a1,n00...0a2,…

Q: find the amount of odd three-digit numbers that can be created. (

A: here given digits are  [0, 1, 2, 3, 4, 5, 6]. so there are total 7 digits . here use counting…

Q: Which are binary operations? E xplain who or why not . A) On the positive integers ,that is ,…

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Q: - (a) In Dn, show that a*bak = b for all k € Z. Please proove using induction, the first variable is…

A: Given : Dihedral group Dn. To show : akbak=b    ∀k∈ℤ.

Q: Use the Second Principle of Finite Induction to establish that for all n is greatre than or equal to…

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Q: The expression m(m-1)a, +x> ka,x is equivalent to the sum whose generic N=2 k=1 term involves x" is…

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Q: Prove that for all natural numbers k, a (5*2^(2k+1) - 1)/3 + a*4^k is of the form 5 + 6a.

A: The question looks incorrect and cannot be proved. This is because of the following.…

Q: If In(a) = 2, In(b) = 3, and In(c) = 5, evaluate the following: %3D ) a-1 (a) In -12 b-3c-1 (b) In…

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Q: If n is a positive integer, then prove that 2n(2n-1) 2n(2n-1)(2n-2) 2! 3! 1-2n+- + ...

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Q: A knight on a chessboard can move one space horizontally (in either direction) and two spaces…

A: Consider the provided question, We have to proof: The knight can visit every square. Proof by…

Q: Prove by induction that for positive integers n, 13|(4^(2n+1)+3^(n-1) )

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Q: Prove that for all natural numbers k, a (4^k - 1)/3 + 2*a*4^k is of the form 1 + 6a

A: We show that the question doesnt hold for a=1 and k=1

Q: select the description that characterizes the Boolean expression

A: A boolean expression is CNF (Conjunctive normal form) if it is a product of sums. And, a boolean…

Q: Show by induction that for each positive integer k, 1?+ 2² + 3² + . . · +k² = }k(k+ 1)(2k + 1).

A: NOTE: Refresh your page if you can't see any equations. . check for k=1 the statement is true…

Q: Find Ax Bx C where A = {1,5}, B={13,17} , C={0}. O (1,13, 0), (1, 17, 0), (5, 13, 0), (17, 5, 0) O…

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Q: Suppose X~N (μ,σ') then X – H - - N (0, 1) o2 O True O False

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Q: 1. Determine whether or not the expressions below are wff (well-formed formulae). Explain your…

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Q: 13. Pier Fermat (1601 – 1665) conjectured that any number F, of the form 2²" + 1 where n is…

A: Fermat number is Fn=22n+1

Q: 28. Let S be the subset of the set of ordered pairs of integers defined recursively by Basis step:…

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Q: 1. Prove that for all numbers of k, (5*2^(2k+1) - 1)/3 is an odd number.

A: Let the given statement is        For k = 1 we get this as    is an odd number…

Q: If a₁, a2, a3, a4 are the coefficients of any four consecutive terms in the expansion of (1 + x)",…

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Q: Prove by induction that for positive integers n:  4|(5^(n+1)+ 3^(2n-1)).

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