Mid Term Question
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MTH001 ASSIGNMENT NO. 1 FALL 2022 |
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the solution of this assignment:
(1) To solve this assignment, you should have
good command over 1 to 5 lectures.
(2) Try to consolidate your concepts that you
learn in the lectures with these questions.
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(4) First of all,
you should download the uploaded question file. Next, solve the given questions
(i.e. type the solution) on it. Finally, submit your own
solution file in VULMS.
Ø
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(requirements) of the questions.
Ø If you do not
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the marks will be deducted (or could be zero).
(5)
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(6)
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Ø Corrupt files will be given zero
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(7) This is an individual assignment (not a group
assignment). So keep in mind that you are supposed to submit your own,
self-made and different assignments even if you discuss the questions with your
class fellows. All the similar assignments (even with some meaningless
modifications) will be awarded zero marks and no excuse will be accepted. This
is your responsibility to keep your assignment safe from others.
Up to 50% marks might be deducted for those assignments which are received after the due date.
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Question: 1 Marks:
10
Verify by using the laws of
logic whether the following statement is a Tautology or not:
~`\(\~q\to p)\to\~\q`
Solution:
Solution
~`\(\~q\to p)\to\~\q`
~`\(\~q v
p)\to\~\q`
`\(q v p)\to\~\q`
`\(q v p) v \~\q`
`\(p v q) v \~\q`
`\p v (q v
\~\q)`
`\p v t`
`t`
So, the given statement is Tautology
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Question: 2 Marks:
10
Using the truth table,
determine whether the following argument form is valid or invalid:
`\p \to \q`
`\p v r`
`\therefore r`
Solution:
Type your solution here.
|
p |
q |
r |
Premise |
Conclusion |
|
|
`\p \to \q` |
`\p v r` |
r |
|||
|
T |
T |
T |
T |
T |
T |
|
T |
T |
F |
T |
T |
F |
|
T |
F |
T |
F |
T |
T |
|
T |
F |
F |
F |
T |
F |
|
F |
T |
T |
T |
T |
T |
|
F |
T |
F |
T |
F |
F |
|
F |
F |
T |
T |
T |
T |
|
F |
F |
F |
T |
F |
F |
The
following argument form is invalid because of both the premise are true but
conclusion is false.
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