Theorem-G satises the right and left cancellation laws
Let G be a group. (i) G satises the right and left cancellation laws; that is, if a; b; x ≡ G, then ax = bx and xa = xb each imply that a = b. (ii) If g ≡ G, then (g-1)-1 = g.
Let G be a group.
(i) G satises the right and left cancellation laws; that is, if a; b; x ≡ G, then ax = bx and xa = xb each imply that a = b.
(ii) If g ≡ G, then (g-1)-1 = g.
Expert
Proof:
(i) From ax = bx, we have axx-1 = bxx-1, then ae = be, then a = b. Similarly for the other case.(ii) Temporarily denote the inverse of g-1 by h (instead of (g-1)-1). Then the defining property of h, from the axiom for inverses applied to g-1, is that
g-1h = hg-1 = e:
But g itself satises these equations in place of h, because the axiom for inverses applied to g says that
gg-1 = g-1g = e:
Hence, since inverses are unique, h = (g-1)-1 = g, as required.
Wffs (Well-formed formulas): These are defined inductively by the following clauses: (i) If P is an n-ary predicate and t1, …, tn are terms, then P(t1, …, t
What is an Ordinary Differential Equation (ODE)?
8. Halloween is an old American tradition. Kids go out dressed in costume and neighbors give them candy when they come to the door. Spike and Cinderella are brother and sister. After a long night collecting candy, they sit down as examine what they have. Spike fi
is the n-Dimensional Qn Hamiltonian? Prove tour answer
For queries Q1 and Q2, we say Q1 is containedin Q2, denoted Q1 C Q2, iff Q1(D) C Q2
Consider the following system of linear equations. (a) Write out t
A cricketer cn throw a ball to a max horizontl distnce of 100m. If he throws d same ball vertically upwards then the max height upto which he can throw is????
Who developed a rigorous theory for Brownian motion?
An oil company blends two input streams of crude oil products alkylate and catalytic cracked to meet demand for weekly contracts for regular (12,000 barrels) mind grade ( 7,500) and premium ( 4,500 barrels) gasoline’s . each week they can purchase up to 15, 000
Mathematical and theoretical biology is an interdisciplinary scientific research field with a range of applications in the fields of biology, biotechnology, and medicine. The field may be referred to as mathematical biology or biomathematics to stress the mathematical
18,76,764
1952370 Asked
3,689
Active Tutors
1429910
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!