Unit 12 Answers

**1.**
x
*A* = {(*x, y*) | *x*
and *y*
*A*} =
=
{(*x, y*)| *x*
*A* and *y*
} =
*A* x

**2.** *mn*

**3.**

- (0, 1, 2, 3, 4, 5}
- {3}
- {1, 2, 4}
- {0, 5}

**4.**

a) *B *
A.
For since * A *
*B = A*
every element of *B * is also in *A *. But * A * may have more
elements than * B *.

b) *A *
*B* =
.
For *A - B = A* means that subtracting elements of *B* does not change
*A*. Hence no elements of *B* are in *A*. Hence *A* and
*B* have no elements in common.

**5.** *A *
*B*
*x* (*x *
*A *
*x *
*B *)
*x* (*x *
*B*
*x*
*A*)
*x*(*x *
*x*
)