Mth202 Assignment solution 2018

Question #1:
Show that the following argument form is invalid:
p → q
~p
∴ ~q

Sol:
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

In the first critical row, the conclusion is false when the premises are true. Therefore, the argument is invalid.






Question #2:
Let A and B be subsets of U, then prove:


(A U A)' = A' ⋂ A'

Sol:
A B A U A (A U A)' A' B' A' ⋂ B'
1 1 1 0 0 0 0
1 0 1 0 0 1 0
0 1 1 0 1 0 0
0 0 0 1 1 1 1