# Discrete Math Problems (Math Problem Sample)

The task involve solving dicrete math problems. There were a number of problems in the task that were to be computed. The sample provides model solution for the various problems in the tasks including using de'morgans laws, performing binary conversions of numbers and calculation of computation memory in computers. step by step solution was presented for each problem.

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Discrete Math: Problems of Week 2

Student’s Name

Institutional Affiliation

Date

1 You encounter two natives C and D but only C speaks. C says: "Both of us are Knaves." What are C and D?

If C is a knight, He is a knave. //This is a contradiction

Therefore, C is a knave.

Since C is a knave, his statement must be false.

Therefore, D is a knight.

2 A set of premises and a conclusion are given. Deduce the conclusion from the premises using the valid argument forms. For full credit, make sure to give a reason for each step.

(a) p ˅ q // Considering premises p and q

(b) q -> r // if the fire was started by an electrical fault, electrical devices were left ON

(c) p ^ s -> t //consider premises p, s, t

(d) ~r// consider premise u

(e) ~q -> u ^ s//

∴ t// the fire was started through smoking

For the argument, we can use the following statements:

P – The fire was started by an individual

q- the fire was started by an electrical fault

r- electrical devices were left while ON

s- the victim was a smoker

t- the fire was started by through smoking

u- the room had no electrical devices except lighting

3 Perform the following arithmetic:

* FFF16 + ACE16

FFF16

+ ACE16

1ACD16

F+E = 29 > 16*1 + D (13)

1+F+C = 28 > 16*1 + C (12)

1+F+A = 26 >16*1 + A (10)

* C08.616 – A2F.D16

C08.616

– A2F.D16

1638.316

6 + D =19 > 16*1 + 3

9 + F = 24 > 16*1 + 8

1+0+2 = 3

C + A = 22 > 16*1 + 6

* 4318 + 1778

4318

+ 1778

6308

1+7=8 >8*1 +0

1+3+7 = 11 >8*1 +3

1+4+1 =6

* 106.38 – 27.58

106.38

– 27.58

56.68

8+3-5=6

8+5-7=6

8-1-2=5

4 right55880000164338058102500Given 0100 1001 0101 0010, tell what characters are stored in main memory. Assume our computer uses 8 bits (ASCII) for characters.

0

1

0

0

1

0

0

1

0

1

0

1

0

0

1

0

27

26

25

24

23

22

21

20

27

26

25

24

23

22

21

20

0

64

0

0

8

0

0

1

0

64

0

16

0

0

2

0

73 82

ASCII Equivalent: IASCII Equivalent: R

Characters stored: IR

5 Find the internal representation of the following decimal numbers. Assume that our computer uses 16 bits for binary integers.

* 254

Divisor

Value

Remainder

2

254

2

127

0

2

63

1

2

31

1

2

15

1

2

07

1

2

03

1

2

01

1

0

1

The representation = 0000 0000 1111 1110

* -254

The internal representation in this case will b

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