Matematisk Lingvistik VT96:06

Class:   06
Date:    960201
Topic:   Exercise class 2

Exercise class 2

These exercises are supposed to be handed in on Monday February 5.

Because of the limitation of the range of characters in HTML I cannot display every character I need. I will use the following replacements in this exercise:

R-1 means the inverse of relation R
idA means the identity relation over set A
F o G means the composition of F and G

In these exercises we will use two sets and two functions:

A = { 1 , 2 , 3 }
B = { 3 , 4 }
F = { <1,3> , <2,3> , <3,4> } , F is a function from A to B
G = { <3,3> , <4,2> } , G is a function from B to A

1. compute A x B

2. compute ( B - A ) x ( A - B )

3. compute R = { <a,b> | a is an element of A and b is an element of B and a < b }

4. determine if the relation R which you have computed in the previous exercise is a subset of (and possibly equal to) A x B

5. determine if this R is a function from A to B

6. compute R-1 and R' (U=AxB)

7. determine if F is into and determine if it is onto

8. determine if G is one-to-one and determine if it is many-to-one

9. compute G o F (the order has been changed)

10. compute F o idA

Each exercise is worth 1 point.