MTH202
- Discrete MathematicsAssignment 1 Solution
Spring
2018
Question 1:
Use the truth table to test the validity of
the following argument
If you invest in the HBFC, then you
get rich.
You didn’t invest in the HBFC.
Therefore, you didn’t get rich.
Solution:
First symbolize the argument.
Let p be the argument”you invest in the HBFC”.
Let q be theargument”you get rich”.
Then the argument has this symbolic form
p → q
~ p
|
p
|
q
|
p → q
|
~p
|
~q
|
|
T
|
T
|
T
|
F
|
F
|
|
T
|
F
|
F
|
F
|
T
|
|
F
|
T
|
T
|
T
|
F
|
|
F
|
F
|
T
|
T
|
T
|
~q
Interpret the
truth table.
This tells us the
argument is INVALID.
Question 2:
Prove that the statement
is tautology.
Solution:
|
p
|
q
|
~p
|
~q
|
p → q
|
~ q ^ (p → q)
|
~ q ^ ( p → q ) → ~ p
|
|
T
|
T
|
F
|
F
|
T
|
F
|
T
|
|
T
|
F
|
F
|
T
|
F
|
F
|
T
|
|
F
|
T
|
T
|
F
|
T
|
F
|
T
|
|
F
|
F
|
T
|
T
|
T
|
T
|
T
|
Hence,
~ q ^ ( p → q ) → ~ p = ‘ t ’
All
truth value of statement is equal to ‘ t ’
So
it is tautology.
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