Homework Assignment 4, Math 70 Fall 2022
Due at 11:59 PM Tuesday, November 29, 2022 submit as a single PDF through the Canvas Assignment
“Homework 4 Submission Portal”
No late assignments accepted. ?” point for NO NAME
1. Construct each of the following Power Sets.
(a) (3 points) P ?g?
(b) (4 points) P ?P ?g??
2. (10 points) In class we considered the set W ?+à,à- ? and all the subsets of W which we defined as
? g E F G H I J W
g ??, E ?+?, F ?,?, G ?- ?,
H ?+à,?, I ?+à- ?, J ?,à- ?, and
g
g E F G H I J W
W ?+à,à- ?.
E E E H I H I W W
Thus the Power Set of W is
F F H F J H W J W
P ?W ? ?gàEàFàGàHàIàJ àW ?
G G I J G W I J W
We formed the Boolean Algebra with the set P ?W ?
H H H H W H W W W
and the operations ? and ? . In class I constructed
I I I W I W I W W
the table on the right that describes the binary
J J W J J W W J W
operation ? .
W W W W W W W W W
Complete the table below that describes the binary operation ?
? g E F G H I J W
g
E
F
G
H
I
J
W
W
3. Consider the function J ?!à”? ?!à”? given by J +`” ? +
(a) (2 points) Draw an arrow diagram that displays this information.
(b) (2 points) Find J ?” .
4. (2 points each) The function K ?+à,à-à.à/? ?+à,à-à.à/?
is given by the arrow diagram on the right.
(a) Find K?” .
(b) Find K .

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