# My Noted

## My Noted

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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