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Boolean Expressions and Truth Tables Part 1-Basic Mathematics-Assignment Solution, Exercises of Mathematics

This is solution to assignment of Basic Mathematics course. This was submitted to Karunashankar Sidhu at Institute of Mathematical Sciences. It includes: Boolean, Expressions, Truth, Table, Argument, Validity, True, False, Premises, Rows, Critical

Typology: Exercises

2011/2012

Uploaded on 08/03/2012

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Solution Of Assignment 1 Of MTH202 (Spring 2012)
Maximum Marks: 15
Question 1; Mark: 10
Formulate the argument symbolically and test its validity using the truth table. Also
mention the critical row (or rows).
If you finish your home work, then you will sleep early.
If you will sleep early, then you will get up for 8:30am class.
Therefore if you finish your home work, then you will get up for 8:30am class.
Where p = you finish your home work,
q = you will sleep early,
r = you will get up for 8:30am class.
Solution:
Given that
p = you finish your homework,
q = you will sleep early,
r = you will get up for 8:30am class
So,
According to first premise p q
According to second premise q r
And conclusion will be p r
Truth Table:
P Q R P q qr pr
T T T T T T
T T F T F F
T F T F T T
T F F F T F
F T T T T T
F T F T F T
F F T T T T
F F F T T T
Where colored rows represents critical rows and they indicate valid (true)
premises. Therefore the above argument form is valid.
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Solution Of Assignment 1 Of MTH202 (Spring 2012)

Maximum Marks: 15

Question 1; Mark: 10

Formulate the argument symbolically and test its validity using the truth table. Also mention the critical row (or rows).

If you finish your home work, then you will sleep early. If you will sleep early, then you will get up for 8:30am class.

Therefore if you finish your home work, then you will get up for 8:30am class.

Where p = you finish your home work, q = you will sleep early, r = you will get up for 8:30am class. Solution:

Given that p = you finish your homework, q = you will sleep early, r = you will get up for 8:30am class So, According to first premise p  q According to second premise q  r And conclusion will be p  r Truth Table:

P Q R P q qr pr T T T T T T T T F T F F T F T F T T T F F F T F F T T T T T F T F T F T F F T T T T F F F T T T

Where colored rows represents critical rows and they indicate valid (true) premises. Therefore the above argument form is valid.

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Question 2; Marks: 5 Construct circuit for Boolean expression (Mention output at each step) (P~ Q)  (P  Q) Solution:

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