conditional statement Need Help Please

Question

If the conditional statement “If I use my cell phone too much, my bill will be expensive,” is true, which other statement must also be true?

Group of answer choices

a.If my bill is expensive, I used my cell phone too much.

b. If I do not use my cell phone too much, my bill will not be expensive.

c.None must be true.

D. If my bill is not expensive, I did not use my cell phone too much.

Answer 1

It can be shown that a conditional statement of the form if p, then q is logically equivalent to its contrapositive.

The contrapositive has the form if not q, then not p.

In this problem "p" has the value: I use my cell phone too much.

"q" has the value "my bill will be expensive".

So the logically equivalent contrapositive of the initial conditional will be:

If bill not expensive, then i do not use my cell phone too much.

Here is another simple example:

Conditional: : if 5x = 10, then x= 2.

Contrapositive: if x ≠ 2, then 5x ≠ 10.

Answer 2

For conditional statement and its contrapositive, they are logically equivalent.

That means if the conditional is true, then the contrapositive will also be true.

Given statement: If p, then q.

Contrapositive: If not q, then not p.

The two parts of the conditional change places and not is inserted into both areas.

The part that says "my bill will be high" will become the if part of the conditional and add not.

The part that says " I use my cell phone too much" will now follow the word then and also add the word not.

The correct answer is D.