Question

Is ~(p—q) equivalent to (~p)—q ? Justify.​

Answer 1

Answer:

p=1

q=0

(p-q)=1

~(p-q)=0

~p=0

0-0=0

Answer 2

Answer:

~(p - q) is equivalent to (~p) - q

Step-by-step explanation:

We need to show if ~(p - q) is equal to (~p) - q

We will check this using a truth table.

First of all, taking the left hand side, i.e. ~(p - q)

p     q       p - q        ~(p - q)

0     0          0                1

0     1           1                 0

1      0          1                 0

1       1          0                1

Now, finding the right hand side, i.e. (~p) - q

p       ~p        q          (~p) - q

0         1         0              1

0         1          1              0

1          0        0              0

1          0         1               1

Now as all the values of ~(p - q) and (~p) - q are equal,

~(p - q) is equivalent to (~p) - q