- Submitted By: Oluwaseun-Odesanya
- Date Submitted: 08/16/2016 7:17 PM
- Category: Business
- Words: 416
- Page: 2

ITNB2103 Discrete Mathematics

Semester October 2015

Name:ALESHINLOYE ZAINAB LABI

Matric: MC1502BC8978

1 Convert the following hexadecimal numbers to decimal numbers.

a DE516

13*16”+14*16+5= 437

b 2AB.416

2*16+10*16+11+4*256 =1227

2) Convert binary 110100100010000 to octal.

Ans: 644208

3) Determine whether the following are propositions. Give the truth value of the propositions.

c 4 + x = 5 is not a statement

d 2 * 3 = 5 is not a statement

c)You will fail this course if you fail the final final exam.

Ans: Is a statement.

4) Give the converse, inverse and contrapositive of this conditional statement.

“ If you have not fed the cat, then the cat is hungry.”

ANS: Converse

If the cat is hungry then I have not fed the cat.

ANS:Inverse

If I have fed the cat, then the cat is not hungry.

ANS: Contrapositive

If the cat is not hungry then I have fed the cat.

5) Find the truth value of each proposition if p and r are true and q is false.

a (p r) → q

P

R

Q

P v r

(p v r) -> q

T

T

T

T

T

T

T

F

T

F

T

T

T

T

F

T

f

T

b) ((p r) → q) → ((p → q) (p → r))

P

R

Q

P v r

(p v r) -> q

(p -> q)

(p -> r)

(p -> q) v (p -> r)

(p v r) -> q) -> (p -> q) v (p -> r)

T

T

T

T

T

T

T

T

T

T

F

T

T

T

T

F

F

T

T

T

T

T

F

F

T

T

F

T

F

T

T

F

F

F

T

F

F

T

T

T

T

T

T

T

T

F

F

F

F

T

T

T

T

T

F

T

T

T

F

T

T

T

F

F

F

F

F

T

T

T

T

T

c) ((¬ p q) r) ( r → ¬ q)

P

Q

R

7p

7q

7p v q

((7p v q ) 0 r)

(r -> 7q)

((7p v q) 0 r) -> (r -> 7q)

T

T

T

F

F

T

F

F

T

T

T

F

F

F

T

T

T

T

T

F

T

F

T

F

T

T

T

T

F

F

F

T

F

F

T

T

F

T

T

T

T

T

F

F

T

F

T

F

T

T

T

T

T

T

F

F

T

T

F

T

F

T

T

F

F

F

T

F

T

T

T

T