Let f: Q8 to D8 be a homomorphism from the quaternion Q8 to the
dihedral group D8 of order 8. Suppose that f (i) = rs and f( j) =
r^2.
(a) Find f (k) and f(-k) (expressed in standard form r^i*s^i for
suitable i and j) ·
(b) List the elements in the kernel of f in standard form.
(c) The quotient group Q8/ker(f) is isomorphic to which one of
the groups C2, C4 or C2xC2 why?
a.) Write down the formulas for all homomorphisms from Z10 into
Z25.
b.)Write down the formulas for all homomorphisms from Z24 into
Z18.
c.)Write down the formulas for all homomorphisms from Z into
Z10.
d.)Extra: Define φ : C x → Rx by φ(a + bi) = a 2 + b 2 for all a
+ bi ∈ C x where R is the real numbers and C is the complex
numbers. Show that φ is a homomorphism.
Q8 From a consequentialist perspective, is the introduction of
payments to support households and income during the COVID-19
crisis (described above) ethically justified?
Q9 Using a deontological ethical framework, construct an
argument either in favour of the payments to support households and
income during the COVID-19 crisis (described above) or against
them.
Q10 Evaluate the introduction of the payments to support
households and income during the COVID-19 crisis (described above)
from the perspective of substantive and procedural judgements of
fairness.