Answer:
q->~p
Step-by-step explanation:
The symbol "~" means "no"
Then:
p → ~q
means:
"if p, then NO q"
or:
"if p, then don't q"
or:
"if p, then ~q"
a better example can be if we define p and q as:
p = n is positive
q = n is zero.
~q = n isn't zero.
~p = n isn't positive.
Then the sentence would be:
"if n is positive, then NO n is zero"
or:
"if n is positive, then n isn't zero"
(the syntaxis is weird, but you can understand this)
Now we need to find an equivalent statement to this one.
Let's look at the given options, and let's try them with our hypothesis and conclusion written above.
p -> q)
"if n is positive, then n is zero"
This obviously is not equivalent.
~p->q)
"if n isn't positive, then n is zero"
Well, n could be negative, then this sentence is false, so it is not equivalent to the original one.
q->p)
"If n is zero, then n is positive"
This is not equivalent to p -> ~q
q->~p)
"if n is zero, then n isn't positive"
This is true, if n = 0, n can not be a positive number.
Then when p -> ~q is true, also q->~p is true, which means that the statements are equivalent.
