Group Theory
Q11.
For the composition table of a cyclic group shown below Which one of the following choices is correct?Q12.
Let P, Q and R be sets, let \triangle denote the symmetric difference operator defined as P\triangle Q=(P \cup Q) - (P \cap Q). Using Venn diagrams, determine which of the following is/are TRUE? I. P \Delta(Q \cap R)=(P \Delta Q) \cap(P \Delta R) II. P \cap(Q \cap R)=(P \cap Q) \Delta(P \Delta R)Q14.
The set {1, 2, 3, 5, 7, 8, 9} under multiplication modulo 10 is not a group. Given below are four plausible reasons. Which one of them is false?Q15.
Some group (G, o) is known to be abelian. Then, which one of the following is true for G?Q16.
Let \left(Z, *\right) be an algebraic structure where Z is the set of integers and the operation * is defined by n*m = \max(n,m). Which of the following statements is true for \left(Z, *\right)?Q17.
Two girls have picked 10 roses, 15 sunflowers and 15 daffodils. What is the number of ways they can divide the flowers among themselves?Q19.
Consider the set \Sigma ^{*} of all strings over the alphabet \Sigma ={0,1}. \Sigma ^{*} with the concatenation operator for stringsQ20.
Consider the set H of all 3 x 3 matrices of the type \begin{bmatrix} a & f & e\\ 0 & b & d\\ 0&0 & c \end{bmatrix} where a,b,c,d,e and f are real numbers and abc\neq0. Under the matrix multiplication operation, the set H is: