MTH202 Discrete Mathematics Assignment No.1 Solution Spring Semester 2013

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[SIZE="4"]MTH202 Discrete Mathematics Assignment No.1 Solution Spring Semester 2013 [/SIZE]

Assignment 1 Of MTH202 (SPRING 2013)
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 Editor etc 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 student of Computer Science. q = I work hard. Then translate the following logical expressions into English sentences.

( ) Use the result: ~ ( p q ) = p ~ q
p q qp pq pq qp pq → → ↔ → → → → ∧ ∼∼ ∼∼ ∼


Q3: Let h = Asad is happy. s = Asad is sad. t = Asad watch television. Then translate the following logical expressions into English sentences.

hts st th t h s t h 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 a p q b c d e f g