B. Prove each item (Item 3 & 4) of the following by constructing a proof by element arguments 3. (RNS)' = R'US' (De Morgan's Law) 4. (M-K) U (L-K) = (M U L)-K

Q: 1,5 1 0.5 0 U do 0.9 -0.9 0.7 -0.7 0.5 -0.5 0.0.1 -0. -0.3 -1 -0.5 0 0.5 1 Let F be the gradient…

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Q: 4. Let a, b, c, d, n € Z such that a = b (mod n) and c= d (mod n). (a) Prove that a+c=b+d (mod n).…

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A: Given that A is 4×4 and invertible matrix. To describe the null space of the 4×8 matrix B=AA. Null…

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Q: tions gn [0, 1] → R given by : Consider the sequence of func- In (x)= = lim gn- (a) Show that (gn)…

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Q: 5. What is the Laplace transform of the given function f(t) = cos³ (t)? 3 S - . 4 s² +9 A) F(s) B)…

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Q: Theorem 4.17. Let m, n be two odd positive integers such that (m, n) = 1. Then we have () () = (-¹)…

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Q: 6. How many ways can the letters of VESTIBULAR be arranged if all the vowels must be adjacent?

A: Given word is VESTIBULAR.

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Q: Rewrite each equation as requested. (a) Rewrite as an exponential equation. ln 8= y (b) Rewrite as a…

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Q: -E (B₁ Cos 2t + B₂ Sinat) é e fit) = 122+ (B₁ Cos 2t +

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Q: Consider the graph given below. u X 9 a. What is the degree of vertex t? b. What is the degree of…

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Q: 1. (Q-R) n (R-S) = Ø 2. [(CND) U (D'n c')] = (C + D)'

A: This is a question of Propositional Logic.

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Q: 9. Prove that if n = 3 (mod 4), then the equation x² + y² = n has no integer solution.

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Q: 5. Given that 13¹² = 1 (mod 21), compute the remainder of 13¹45 when divided by 21.

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Q: Write (-3-3√//3i)5 in trigonometric form. O 248832 (cos 4+ i sin 4) 3 2π O 31104 √2 (cos 2 + i sin…

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Q: The following table gives the number of fatal work injuries categorized by cause from 2015 in a…

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Q: Question Let C' be the circle centered at the origin with radius 4 oriented clockwise, and let F(x,…

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