The document presents a series of logic and circuit problems in computer science, including Boolean algebra, Karnaugh maps, and validity of statements. Various questions involve evaluating premises and conclusions, along with mathematical calculations pertaining to truth values. Additionally, it explores logical expressions and sets in a structured format.

1. Computer Science - Logic, sets, Boolean algebra, Karnaugh maps and circuits
Question 1 PART A
i)
b r
g r
g TRUE
→ ¬
¬ →
→
Conclusion: b∴
ii
b g r b r→ ¬ g r¬ →
0 0 0 1 0
0 0 1 1 1
0 1 0 1 1
0 1 1 1 1
1 0 0 1 0
1 0 1 0 1
1 1 0 1 1
1 1 1 0 1
iii
Statement is invalid because there exists a situation where conclusion is false even
though all the premise are true
For example Line 3: Giraffes are green, therefore g r¬ → is satisfied but then b can
not be satisfied.

2. Question 1 Part B
Let r = System is Ready
Let l = Light is on
1. r l¬ → ¬
2. r l¬ ∨ ¬
3. r l→
4. r l¬ ∨
5. l r→
6.l r→ ¬
7. r l→ ¬
8. l r¬ ∨
9. l r¬ → ¬
Group 1: (1,5,8)
Group 3: (2,6,7)
Group 2: (3,4,9)

3. Question 2
Part a:
Part b
i) 13+19+18=50
ii) 9
iii) 22+19+14=55
iv) 22+19+14+12=67

4. Question 3
1. , , ( , )p m S p m∀ ∀
2. , ,~ ( , )p m S p m∃ ∀
3. , ,~ ( , )m p S p m∃ ∀
4. , , ( , )m p S p m∃ ∀
5. , ,~ ( , )m p S p m∀ ∀
6. , ,~ ( , )m p S p m∃ ∃
7. , , ( , )p m S p m∃ ∀
8. , ,~ ( , )m p S p m∀ ∃
9. , , ( , )p m S p m∀ ∃
10. , ,~ ( , )p m S p m∀ ∃
11. , , ( , )m p S p m∀ ∃
12. , , ( , )m p S p m∃ ∃
Answer:
1,6
2,9
3,11
4,8
5,12
7,10
Question 4
i) 0110000100001000
ii) {Chad, Eritrea, Ghana, Rwanda, Sudan, Zambia}
Part iii
P 0 1 1 1 0 1 0 1 0 1 1 0 1 0 0 1
Q 0 1 0 1 0 0 1 1 1 0 1 0 1 0 1 1
R 1 1 0 1 1 1 0 0 0 1 0 0 1 1 1 0
S 1 1 0 1 0 1 1 0 1 0 0 1 1 0 0 1
P' 1 0 0 0 1 0 1 0 1 0 0 1 0 1 1 0
S' 0 0 1 0 1 0 0 1 0 1 1 0 0 1 1 0
(P' AND Q) 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0
(R AND S') 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0
Union(Answer
) 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0
Part iv
{Etriera,Kenya,Mail,Nambia,Uganda,Zaire}

5. Question 5
SEGMENT D
Key w x y z d FP
0 0 0 0 0 1 w'x'y'z'
1 0 0 0 1
2 0 0 1 0 1 w'x'yz'
3 0 0 1 1 1 w'x'yz
4 0 1 0 0
5 0 1 0 1 1 w'xy'z
6 0 1 1 0 1 w'xyz'
7 0 1 1 1
8 1 0 0 0 1 wx’y’z’
9 1 0 0 1 1 wx'y'z
A 1 0 1 0
B 1 0 1 1 1 wx'yz
C 1 1 0 0 1 wxy'z'
D 1 1 0 1 1 wxy'z
E 1 1 1 0 1 wxyz'
F 1 1 1 1
y y
1 1 1
1 1 x
w 1 1 1 x
w 1 1 1
z z
yx+ wy`+ w`yx` +w’x’y’z’+w’xy’z +wx’yz

6. Question 5
SEGMENT G
Key w x y z g FP
0 0 0 0 0
1 0 0 0 1
2 0 0 1 0 1 w'x'yz'
3 0 0 1 1 1 w'x'yz
4 0 1 0 0 1 w'xy'z'
5 0 1 0 1 1 w'xy'z
6 0 1 1 0 1 w'xyz'
7 0 1 1 1
8 1 0 0 0 1 wx'y'z'
9 1 0 0 1 1 wx'y'z
A 1 0 1 0 1 wx'yz'
B 1 0 1 1 1 wx'yz
C 1 1 0 0 1 wxy'z'
D 1 1 0 1 1 wxy'z
E 1 1 1 0 1 wxyz'
F 1 1 1 1 1 wxyz
y y
1 1
1 1 1 x
w 1 1 1 1 x
w 1 1 1 1
z z
W+ w’xy’z+z’x +w’x’y

7. Question 5
SEGMENT G
Key w x y z g FP
0 0 0 0 0
1 0 0 0 1
2 0 0 1 0 1 w'x'yz'
3 0 0 1 1 1 w'x'yz
4 0 1 0 0 1 w'xy'z'
5 0 1 0 1 1 w'xy'z
6 0 1 1 0 1 w'xyz'
7 0 1 1 1
8 1 0 0 0 1 wx'y'z'
9 1 0 0 1 1 wx'y'z
A 1 0 1 0 1 wx'yz'
B 1 0 1 1 1 wx'yz
C 1 1 0 0 1 wxy'z'
D 1 1 0 1 1 wxy'z
E 1 1 1 0 1 wxyz'
F 1 1 1 1 1 wxyz
y y
1 1
1 1 1 x
w 1 1 1 1 x
w 1 1 1 1
z z
W+ w’xy’z+z’x +w’x’y