Answer
The statement \[\sim (p\wedge q)\] means that not statement p or not statement q and the statement \[\sim p\wedge q\]means that not statement p and statement q.
Work Step by Step
Consider the provided symbolic statement\[\tilde{\ }\,(p\wedge q)\].
Parenthesis represents negation of both, i.e.,
\[\tilde{\ }(p\wedge q)\equiv (\tilde{\ }p)\vee (\tilde{\ }q)\]
That means not statement p or not statement q.
Consider another provided symbolic statement\[\sim p\wedge q\].
There is no parenthesis.
Thus,
Negation comes only before p:
\[\tilde{\ }p\wedge q\equiv (\tilde{\ }p)\wedge q\]
That means not statement p and statement q.
Example:
Let’s assume two simple statement p and q.
p: Sun rises in the east.
q: \[2+2=4\]
Now, consider the provided symbolic form\[\tilde{\ }(p\wedge q)\].
It represents neither the sun rises in the east nor\[2+2=4\].
Now consider the provided symbolic form\[\sim p\wedge q\].
It represents sun does not rises in the east and\[2+2=4\].
