A Latin square is is an n × n array filled with n different symbols, each occurring exactly once in each row and exactly
Posted: Tue Sep 07, 2021 7:47 am
A Latin square is is an n × n array filled with n
different symbols, each occurring exactly once in each row and
exactly once in each column.
Note that the Cayley table on page 31 is a Latin square. Use
this fact to show:
1) For every x in D4, there exists y in D4 such that
xy=R0.
2) For each of the eight elements x of D4, find the
corresponding y such that xy=R0.
3) For each of the eight pairs x,y from part 2 (where xy=R0),
show that yx=R0. Conclude that for all x,y in D4, if xy=R0, then
xy=yx.
4) For every x,y in D4, xy is also in D4.
5) Show (HV)R90=H(VR90).
6) Show that xR0=R0 x =x for all x in D4.
7) Show that (xy)z=x(yz) for all x,y,z in D4 [Hint: Use the fact
that function composition is always associative.]
8) Find a example of x,y in D4 such that xy and yx are NOT
equal.
different symbols, each occurring exactly once in each row and
exactly once in each column.
Note that the Cayley table on page 31 is a Latin square. Use
this fact to show:
1) For every x in D4, there exists y in D4 such that
xy=R0.
2) For each of the eight elements x of D4, find the
corresponding y such that xy=R0.
3) For each of the eight pairs x,y from part 2 (where xy=R0),
show that yx=R0. Conclude that for all x,y in D4, if xy=R0, then
xy=yx.
4) For every x,y in D4, xy is also in D4.
5) Show (HV)R90=H(VR90).
6) Show that xR0=R0 x =x for all x in D4.
7) Show that (xy)z=x(yz) for all x,y,z in D4 [Hint: Use the fact
that function composition is always associative.]
8) Find a example of x,y in D4 such that xy and yx are NOT
equal.