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Abstract Algebra
Q.1: Do the odd integer form a group w.r.t addition?
Q.2: Do the non-zero positive real number form a group w.r.t multiplication?
Q.2: Do the non-zero positive real number form a group w.r.t multiplication?
Abstract Algebra
Q. Find index of subgroup generated by 3 in Z12.
Abstract Algebra
Q. prove that H={a+ib C, a2+b2=1} is a subgroup of C. Where C is complex number. H be set of real number a+b where a,b Є ф. Show that H be a subgroup of non-zero real no. under multiplication.
Abstract Algebra
Q. Do the even integer form a group w.r.t addition.
Abstract Algebra
Q. Do the non zero positive rational no. form a group w.r.t multiplication.
Abstract Algebra
Q. Do the odd integer form a group w.r.t addition.
Abstract Algebra
Assume that A and B are isomorphic commutative rings with unity. Prove that if A is a field, so is B.
Abstract Algebra
16. 5 The following are true except (a) If every element of a set B is an element of a set A, then B is a subset of A. (b) A is a subset of B is denoted by A⊂B (c) Two sets A and B are equal if and only if A⊆B and B⊆A (d) Two sets A and B are equal if and only if A = -B and B = A
17. If A = { a + i b / a, b ϵ R }, then A is a set of ……… numbers (a) rational (b) natural (c) real (d) complex
17. If A = { a + i b / a, b ϵ R }, then A is a set of ……… numbers (a) rational (b) natural (c) real (d) complex
Abstract Algebra
Let Z be a complex number, then Z.Z ¯ is ........ (a) a prime number (b) a non-negative real number (c) a natural number (d) an irrational number
A ………… of an Abelian group is Abelian (a) set (b) subset (c) group (d) subgroup
One of the following is untrue for the description of a non empty set
(a) An element can be written more than once (b) The order in which the elements of the set are listed is not important (c) The roster method is sometimes used to list the elements of a large set (d) Every element must be written exactly once
A ………… of an Abelian group is Abelian (a) set (b) subset (c) group (d) subgroup
One of the following is untrue for the description of a non empty set
(a) An element can be written more than once (b) The order in which the elements of the set are listed is not important (c) The roster method is sometimes used to list the elements of a large set (d) Every element must be written exactly once
Abstract Algebra
Given a set X={a,b,c}, and a function Ψ:X→X define by Ψ(a)=b,Ψ(b)=a,Ψ(c)=c
. the function is (a)Only unto (b) only injective (c) bijective (d)no solution
A matrix X=(35 12 ) define a function from R 2 toR 2 by f X (a,b)=(3a+b,5a+2b) . find the inverse function of f X (a)f −1 X (a,b)=(3a−b,−5a+3b) (b)f 1 X (a,b)=(2a−b,−5a+3b) (c)f 5 X (a,b)=(2a−b,−5a+3b) (d) f 1 X (a,b)=(2a−b,−5a+4b)
Which of the following is divisible by 17 for all positive integer n (a) 7 n +2 (b) 6 n +2 (c) 2.7 n +3.5 n −5 (d)3.5 2n+1 +2 3n+1
. the function is (a)Only unto (b) only injective (c) bijective (d)no solution
A matrix X=(35 12 ) define a function from R 2 toR 2 by f X (a,b)=(3a+b,5a+2b) . find the inverse function of f X (a)f −1 X (a,b)=(3a−b,−5a+3b) (b)f 1 X (a,b)=(2a−b,−5a+3b) (c)f 5 X (a,b)=(2a−b,−5a+3b) (d) f 1 X (a,b)=(2a−b,−5a+4b)
Which of the following is divisible by 17 for all positive integer n (a) 7 n +2 (b) 6 n +2 (c) 2.7 n +3.5 n −5 (d)3.5 2n+1 +2 3n+1
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#340153 on Dec 2023
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