To form the inverse of a conditional statement, you follow a simple rule. If the original conditional statement is of the form "If p, then q" (symbolically, this can be denoted as p -> q), then the inverse of the conditional statement is "If not p, then not q" (symbolically, this is ~p -> ~q). This involves negating both the hypothesis (p) and the conclusion (q).
Now let’s apply this knowledge to the given conditional statement:
The original statement is: "If a number is doubled, the result is even."
Symbolically, if we let:
- p represent "a number is doubled,"
- q represent "the result is even,"
then the original statement is p -> q.
The inverse of this statement would thus be: "If a number is not doubled, the result is not even."
Symbolically, if we negate both parts, we get:
- ~p represent "a number is not doubled,"
- ~q represent "the result is not even,"
which gives us the inverse as ~p -> ~q.
So, the representation of the inverse of the original statement in the given options is:
"~p -> ~q where p = a number is doubled and q = the result is even."
According to the available options, the correct one is:
1. ~p -> ~q where p = a number is doubled and q = the result is even.
