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- 5) Which of the following are properties of all squares: 1. Congruent diagonals 2. Perpendicular diagonals 3. Diagonals that bisect vertex angles a) 1 and 2 only b) 1 and 3 only c) 2 and 3 only d) 1, 2, and 3arrow_forward6) In an isosceles trapezoid HIJK it is known that IJ || KH. Which of the following must also be true? a) IJ = KH b) HIJK c) HIJK d) IJ KHarrow_forward4) When rectangle JKLM is plotted in the coordinate plane side JK has a slope equal to 3. What must be the slope of side MJ? a) 3/3 b) e 35 53 32 d) - 5arrow_forward
- 4) Find a proposition with three variables p, q, and r that is never true. 5) Determine whether this proposition is a tautology using propositional equivalence and laws of logic: ((p (bv (bL ← →¬p [1 6) Explain why the negation of "Some students in my class use e-mail” is not "Some students in my class do not use e-mail".arrow_forwardMilgram lemma B) Consider Show that -Au= f in a u=0 on on llu-ulls Chllullz 02 Prove that Where ||ul| = a(u, u) = vu. Vu dx + fonu.u ds Q3: Let V = H' (2), a(u,v) = CR, a(u,v) = (f,v) where Vu. Vv dx + Ja cuv dx and ||u|=|||| Show that a(u, v) is V-ellipiticly and continuity.arrow_forward7) Is the following statement True or False: AU BUA = Ā. Justify your answer. 8) Suppose g: A → B and f: B → C where A = {2,3,6,8}, and g and f are defined by g = {a, b, c, d}, B = {1,2,3}, C = {(a,2), (b,1), (c, 3), (d, 2)} and f = {(1,8),(2,3), (3,2)}. Find fog, gof and f−¹. 9) Verify that a₁ = 7(3") -π is a solution to the recurrence relation an = an 4an-1 -3an-2arrow_forward
- 1) Find the prime factorization of 111111. 2) Find (-88 mod 13) 5 mod 7. 3) Use the Euclidean algorithm to find gcd(144,233).arrow_forward3 10) Suppose B = 2 4 5) and C = (b 2 prove that no such matrix exists. (6 1) . Find a matrix A such that AB = C orarrow_forwardi let V-H.) R aluv) = (v) where alu)=SU. V dx and { and (v) sv Show that the finite element solution Un Unique Prove that U-Un ll≤ch llull A²=f and U= Ju =0 on on a with bili near from a (u,v) = SAU. Av dr 32 Prove that aluv) is countinous and V-expitic ii Prove that 2 Mete ||(U-U|| ²== ||||²+|| || ² where -Auf in U=0 on 2arrow_forward
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