MTH001 Elementary Mathematics Assignment 1 Solution Fall 2017

Question No. 1:   Using the truth table, determine the validity of following argument:

If you invest in business, then you get profit.
You didn’t invest in business.
Therefore, you didn’t get profit.

Solution:

P1  if you invest in business, then you get profit

P2  you didn’t invest in business.

⸫c   you didn`t get profit.

P1                 p2                 ⸫c

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

 

This argument is invalid

 

Question No. 2:   Using the truth table, determine whether the following argument is valid or invalid:

Solution

                     P1 :  If x ≤ 0 then x > −1

P2 : x ≤ 0

⸫c   : x >−1

P1                     P2                     ⸫

p

q

p→q

p

q

T

T

T

T

T

T

F

F

T

F

F

T

T

F

T

F

F

T

F

F

 

This argument is valid J

 Question No. 3:   Using truth table, determine whether the statement

        is a Tautology or not?

p q ~p (p→q) ~pv(p→q) ~pv(p→q)→~p
T T F T T F
T F F F F T
F T T T T T
F F T T T T

 

This statement is not tautology

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