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 July 4th, 2018, 11:28 PM #1 Newbie   Joined: Jul 2018 From: india Posts: 1 Thanks: 0 Immediate Help Required in discrete mathematics Hi Friends, I am new to this forum and my son is awfully struck in some discrete mathematics question. Your help is highly solicited. The questions are posted below: 1. Prove that if H, K are subgroups of a group G and H Ų K = G. Then either H=G or K=G 2. Let G be a group and a, b Є G. Then the equation x*a=b has a unique solution given by x= b* a 3. Linear sum W1+ W2 of two subspaces W1and W2 of a vector space V(F) is A subspace of V(F) 4. show that the function T: R2 → R2 such that T(0,1)=(3,4),T(3,1)=(2,2) And T(3,2)=(5,7) is not a L.T. 5. Let T:v →w be a linear transformation. Then T is onto iff p(T)= dim w. 6. show that the function T: R2 → R2 defined by T(x1,x2)=(x1-x2,x1+x2),for (x1,x2)Є R2 is bijective Please provide detailed steps as I do not know these mathematics, but when I give this to my son, he can understand. Thanks in advance friends. July 5th, 2018, 02:15 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,919 Thanks: 2202 2. For a, b ∈ G, where (G,*) is a group, let c ∈ G be the unique inverse of a, then x*a = b implies (x*a)*c = b*c, which simplifies to x = b*c. Note: the usual axioms of a group (G,*) specify that the group operation is associative and that each element of G has an inverse. It's an elementary theorem that no element has more than one inverse. 4. If T is a L.T., T(0,1) + T(3,1) = T(0+3,1+1) = T(3,2) = (5,7), but T(0,1) + T(3,1) = (3,4) + (2,2) = (5,6), not (5,7). 6. T is bijective as it has an inverse Q(x,y) = ((x+y)/2,(y-x)/2). Thanks from zylo Tags discrete, discrete mathematics, group theory, linear transformation, mathematics, required, vector spaces Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post chris7789 Computer Science 0 September 11th, 2017 04:49 PM rntbeats Applied Math 3 November 23rd, 2014 02:38 AM Shruthi318 Applied Math 0 November 9th, 2013 09:42 PM conradtsmith Abstract Algebra 1 April 19th, 2010 07:02 AM conradtsmith Number Theory 1 April 19th, 2010 06:11 AM

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