Saturday 20 April 2013
Assignment 1 Of MTH202 (SPRING 2013)
Maximum Marks: 0
Lectures ( 1 – 4 )
DON’T MISS THESE: Important instructions before attempting the solution of
this assignment:
• Assignment # 1 is non-graded. The questions given in it are for your practice
only. Therefore, you do not need to send the solution of this assignment.
• To solve this assignment, you should have good command over 01 - 04
lectures.
• Try to get the concepts, consolidate your concepts and ideas from these
questions which you learn in the 1 to 4 lectures.
• Use Math Type or Equation Editoretc for mathematical symbols.
Q1:Which of the following are the propositions? Write Truth value of each proposition.
1. Ali is an intelligent boy.
2. She cooks well.
3. 5 + 6 = 12
4. x + 5 > 20
5. The sun sets in the west.
6. Complete your homework.
7. Respect your elders.
8. The set of natural numbers begins with 1.
9. The square root of 2 is irrational.
10. The sky is blue at night.
11. Honesty is the best policy.
Q2:Let p = “I am a studentof Computer Science.”
q = “I work hard.”
Then translate the following logical expressions into English sentences.
()
()
()
()
()
( ) ( ) Use the result: ~ ( p q ) = p ~ q
apq
bq p
cpq
dpq
eqp
fpq
→
→
↔
→
→
→→∧ ∼∼
∼∼
∼
Q3:Let h = “Asad is happy.”
s = “Asad is sad.”
t = “Asad watch television.”
Then translate the following logical expressions into English sentences.
()
()
()
()
()
ah t s
bs t
ct h
dths
eth s
→∧
↔
→
→∨
∧↔
∼
∼
∼∼
∼
∼
Q4:Write converse, inverse, contra-positive of the following conditional sentences:
a. If Ali plays soccer, then Bilal plays hockey.
b. If it is spring season, then trees are green.
c. If x is a natural number, then 2x is an even number.
Q5:Construct the Truth table for ()p q → ∼
( Hint: Use the result: ()p qpq →≡∧ ∼∼)
Q6:What is the Truth value of each of the following logical expressions?
Given : p = True, q = False
( For example: p q = true false = true )
()
( ) ( p q )
( ) p q
( ) p q
( ) q p
( ) q ~ p
( ) p q
apq b
c
d
e
f
g
∨∨
⊕
∧
∨
→
→
→
↔
∼
∼∼
∼
∼
Solution:
ASSIGNMENT # 1(MTH202)
Q1:Which of the following are the propositions? Write Truth value of each proposition.
1.Ali is an intelligent boy. (F) PREPOOSITION
2.She cooks well. NOT A PREPOSITION
3.5 + 6 = 12 (F) PREPOOSITION
4.x + 5 > NOT A PREPOOSITION
5.The sun sets in the west. (T) PREPOOSITION
6.Complete your homework. NOT A PREPOOSITION
7.Respect your elders. NOT A PREPOOSITION
8.The set of natural numbers begins with 1. (T) PREPOOSITION
9.The square root of 2 is irrational. (F) PREPOOSITION
10.The sky is blue at night. (F) PREPOOSITION
11.Honesty is the best policy. (T) PREPOOSITION
Q2: Let p = “I am a student of Computer Science.”
q = “I work hard.”
Then translate the following logical expressions into English sentences.
a) p → q
If i am a student of Computer Science then I must work hard.
b) q → p
If I work hard then I must be Computer Science Student.
c) p ↔ q
If I am a student of Computer Science if and only if I work hard.
d) ~ p → ~ q
If I am not a student of Computer Science then I must not work hard.
e) ~ q → ~ p
if I m not working hard then I must not be a Student of Computer Science.
f) ~ (p → q) Use the result: ~ (p → q) = p ˅ ~ q
I m a student of Computer Science and I don’t work hard.
Q3: let h = “Asad is happy.”
S = “Asad is sad.”
t = “Asad watch television.”
Then translate the following logical expressions into English sentences
a) h → t ˅ ~ s
if Asad is happy then he watch TV and he is not sad.
b) s ↔ ~ t
Asad is sad if and only if he is not watch TV.
c) ~ t → ~ h
If Asad is not watch TV then he is not happy.
d) ~ t → h ˄ s
Asad is not watch TV then he is happy or he is sad.
e) t ˄ h ↔ ~ s
Asad watch TV or he is happy if and only if he is not sad.
Q4: Write converse, inverse, contra-positive of the following conditional sentences:
a: If Ali plays soccer, then Bilal plays hockey.
Converse: If Bilal plays hockey, then Ali plays soccer.
Inverse: If Ali not plays soccer, then Bilal is not plays hockey
contra-positive If Bilal not plays hockey, then Ali is not plays soccer.
b: If it is spring season, then trees are green.
Converse: If trees are green, then its spring season.
Inverse: If it is not a spring season, then the trees are not green.
contra-positive If trees are not green, then its not spring season.
c: if x is a natural number, then 2x is an even number.
Converse: If 2x is an even number, then the x is a natural number.
Inverse: If x is not a natural number, then 2x is not an even number.
contra-positive: If 2x is not an even number, then the x is not a natural number.
Q5: Construct the truth table for ~ (p → q)
(Hint: Use the result : ~ ( p → q ) = ( p ˄ ~ q)
p
|
q
|
~ q
|
p → q
|
~ ( p → q )
|
( p ˄ ~ q)
|
T
|
T
|
F
|
T
|
F
|
F
|
T
|
F
|
T
|
F
|
T
|
T
|
F
|
T
|
F
|
T
|
F
|
F
|
F
|
F
|
T
|
T
|
F
|
F
|
Q6: What is the truth value of each of the following logical expressions ?
Given : p = True, q = False
( For example : p ˅ q = True ˅ False = True )
P
|
Q
|
~p
|
~q
|
p ˄ q
|
p q
|
~ ( p ˄ q )
|
~ q → ~ p
|
p → q
|
~ q → p
|
~ p ˅ ~ q
|
p ↔ q
|
T
|
F
|
F
|
T
|
F
|
T
|
T
|
T
|
F
|
T
|
T
|
