# Difference: EDMExamISampleTest (4 vs. 5)

#### Revision 52011-03-15 - JimSkon

Line: 1 to 1

 META TOPICPARENT name="ElementaryDiscreteMath2011"

# Elementary Discrete Math

###### Sample Exam I
Line: 9 to 9
(a) p → ¬( p ∨¬q)
`<--/twistyPlugin twikiMakeVisibleInline-->`
neither
`<--/twistyPlugin-->`
Changed:
<
<
(b) q ∧ ¬( pq)
`<--/twistyPlugin twikiMakeVisibleInline-->`
`<--/twistyPlugin-->`
>
>
(b) q ∧ ¬( pq)
`<--/twistyPlugin twikiMakeVisibleInline-->`
`<--/twistyPlugin-->`
(c) (( p ∨ ¬p) → q)
`<--/twistyPlugin twikiMakeVisibleInline-->`
neither
`<--/twistyPlugin-->`
Line: 193 to 193
(f) P(A), where A is the power set of {a,b,c}.
`<--/twistyPlugin twikiMakeVisibleInline-->`
256
`<--/twistyPlugin-->`
Changed:
<
<
(g) A x B, where A = {a,b,c} and B = Ø.
`<--/twistyPlugin twikiMakeVisibleInline-->`
0
`<--/twistyPlugin-->`
>
>
(g) A x B, where A = {a,b,c} and B = ∅.
`<--/twistyPlugin twikiMakeVisibleInline-->`
0
`<--/twistyPlugin-->`
(h) {x|x ∈ N and 4x2 - 1 = 0}.
`<--/twistyPlugin twikiMakeVisibleInline-->`
0
`<--/twistyPlugin-->`
Line: 215 to 215
(b) {{a}} ⊆ P(A)
Changed:
<
<
(c) Ø ⊆ A
>
>
(c) ∅ ⊆ A

Changed:
<
<
(d) {Ø} ⊆ P(A)
>
>
(d) {∅} ⊆ P(A)

Changed:
<
<
(e) Ø ⊆ A x A
>
>
(e) ∅ ⊆ A x A
(f) {a,c} ∈ A
Line: 242 to 242
(e) {x | x ∈ Z and x2 < 80}.
Changed:
<
<
(a) 1, (b) 2^(2^3)=256, (c) ¥ ,(d) 24, (e) 17

`<--/twistyPlugin twikiMakeVisibleInline-->`
(a) 1, (b) 2^(2^3)=256, (c) infinity ,(d) 24, (e) 17
`<--/twistyPlugin-->`
>
>
`<--/twistyPlugin twikiMakeVisibleInline-->`
(a) 1, (b) 2^(2^3)=256, (c) ∞ ,(d) 24, (e) 17
`<--/twistyPlugin-->`

Changed:
<
<
16. Let A = { 2,4,6,8 } B = {4, 7} C = {Ø, {4, 7}}
>
>
16. Let A = { 2,4,6,8 } B = {4, 7} C = {∅, {4, 7}}
Show the following:
Line: 255 to 253
b. A ∩ B =
`<--/twistyPlugin twikiMakeVisibleInline-->`
{ 4 }
`<--/twistyPlugin-->`
Changed:
<
<
c. A ∪ C =
`<--/twistyPlugin twikiMakeVisibleInline-->`
{{ 2,4,6,8, Ø, {4, 7}}
`<--/twistyPlugin-->`
>
>
c. A ∪ C =
`<--/twistyPlugin twikiMakeVisibleInline-->`
{{ 2,4,6,8, ∅, {4, 7}}
`<--/twistyPlugin-->`

Changed:
<
<
d. A ∩ C =
`<--/twistyPlugin twikiMakeVisibleInline-->`
Ø
`<--/twistyPlugin-->`
>
>
d. A ∩ C =
`<--/twistyPlugin twikiMakeVisibleInline-->`
`<--/twistyPlugin-->`
e. A - B =
`<--/twistyPlugin twikiMakeVisibleInline-->`
{2, 6, 8}
`<--/twistyPlugin-->`
Changed:
<
<
f. C - Ø =
`<--/twistyPlugin twikiMakeVisibleInline-->`
{Ø, {4, 7}}
`<--/twistyPlugin-->`
>
>
f. C - ∅ =
`<--/twistyPlugin twikiMakeVisibleInline-->`
{∅, {4, 7}}
`<--/twistyPlugin-->`

g. ∅ - C =

`<--/twistyPlugin twikiMakeVisibleInline-->`
`<--/twistyPlugin-->`

Changed:
<
<
g. Ø - C =
`<--/twistyPlugin twikiMakeVisibleInline-->`
Ø
`<--/twistyPlugin-->`
>
>
h. C ∪ (A ∩ B) =
`<--/twistyPlugin twikiMakeVisibleInline-->`
{4, ∅, {4, 7}}
`<--/twistyPlugin-->`

Changed:
<
<
h. C ∪ (A ∩ B) =
`<--/twistyPlugin twikiMakeVisibleInline-->`
{4, Ø, {4, 7}}
`<--/twistyPlugin-->`
>
>
i. P(A) =
`<--/twistyPlugin twikiMakeVisibleInline-->`
{{},{2},{2,4},{2,4,6},{2,4,6,8},{2,4,8},{2,6},{2,6,8},{2,8},{4},{4,6},{4,6,8},{4,8},{6},{6,8},{8}}
`<--/twistyPlugin-->`

>
>
j. B x C =
`<--/twistyPlugin twikiMakeVisibleInline-->`
{(4, ∅), (4, {4, 7}), (7, ∅), (7, {4, 7}) }
`<--/twistyPlugin-->`

17. Show Venn Diagrams for each of the above.

Line: 280 to 281

1. (A ∪ (B ∩ A)) c ∩ ((C c ∪ B c) ∩ A c) c

Changed:
<
<
19. Prove the following using a. set builder notation and b Membership tables
>
>
19. Determine which relationship ⊆, =, ⊇ is true between each pair of sets.

a. A ∩ (A ∪ B), A

`<--/twistyPlugin twikiMakeVisibleInline-->`
=
`<--/twistyPlugin-->`

b. A ∩ (B ∪ C), (A ∪ B) ∩ (A ∪ C)

`<--/twistyPlugin twikiMakeVisibleInline-->`
`<--/twistyPlugin-->`

c. A ∪ (B ∩ C), (A ∪ B) ∩ (A ∪ C)

`<--/twistyPlugin twikiMakeVisibleInline-->`
=
`<--/twistyPlugin-->`

20. Consider the following sets. Pick the correct description. What is the cardinality of each set?

Changed:
<
<
a. A ∩ (A ∪ B) = A
>
>
a. A = {x |x N ∧ (∀y,w : y,w N ∧y ≠ 1 ∧ w ≠ 1 ∧ xyw ) } ( N is the set of natural numbers)
`<--/twistyPlugin twikiMakeVisibleInline-->`
Prime numbers, infinite
`<--/twistyPlugin-->`

Changed:
<
<
b. A ∩ (B ∪ C) = (A ∪ B) ∩ (A ∪ C)
>
>
b. A = {x |x N ∧ x < 100 ∧ (∃y: y N ∧ x = 3y) } ( N is the set of natural numbers)
`<--/twistyPlugin twikiMakeVisibleInline-->`
multiples of 3 {3, 6, 9, ... 99}, 33
`<--/twistyPlugin-->`
-- JimSkon - 2011-03-14 \ No newline at end of file

Copyright &Â© by the contributing authors. All material on this collaboration platform is the property of the contributing authors.
Ideas, requests, problems regarding TWiki? Send feedback