
Abstract Algebra Abstract Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
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)=(x1x2,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: 19,502 Thanks: 1739 
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,(yx)/2). 

Tags 
discrete, discrete mathematics, group theory, linear transformation, mathematics, required, vector spaces 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Need Discrete mathematics help  chris7789  Computer Science  0  September 11th, 2017 04:49 PM 
Discrete Mathematics  rntbeats  Applied Math  3  November 23rd, 2014 02:38 AM 
Discrete Mathematics.  Shruthi318  Applied Math  0  November 9th, 2013 09:42 PM 
discrete mathematics  conradtsmith  Abstract Algebra  1  April 19th, 2010 07:02 AM 
discrete mathematics  conradtsmith  Number Theory  1  April 19th, 2010 06:11 AM 