what is the contrapositive of ~b ->a?
a.) a -> b
b.) ~a -> ~b
c.) ~a -> b
d.) b -> ~a
To find the contrapositive of a logical statement, you need to reverse both the hypothesis and the conclusion, and then negate both.
The given logical statement is ~b -> a.
Step 1: Reverse the hypothesis and the conclusion:
- The hypothesis is ~b, so we reverse it to b.
- The conclusion is a, so we reverse it to ~a.
Step 2: Negate both the hypothesis and the conclusion:
- Negating b gives us ~b.
- Negating ~a gives us a.
Putting it all together, the contrapositive of ~b -> a is ~a -> ~b.
Therefore, option b) ~a -> ~b is the contrapositive of the statement ~b -> a.