163k views
3 votes
X=2 if and only if |x| = 2
True or false? Please answer if you're 100 percent sure.

User Stan Shaw
by
8.3k points

1 Answer

4 votes

Answer:

False

Explanation:

Let's just analyze it.

x=2 if and only if |x|=2

That can be rewritten as:

if x = 2 then |x| = 2

AND

if |x| = 2 then x = 2

Let's solve each one separately:

we have x = 2

we can simply get |x| by removing the sign, if any. There is none, so |x| = 2.

The first part checks out.

we have |x| = 2

As with absolute values, this means that either x = 2 or x = -2

So we know from |x| that x is either 2 or -2, but the logical statement said "if |x| = 2 then x = 2", which is too specific - it forgets about -2.

The second part is false.

Overall, we now know that "X=2 if and only if |x| = 2" is false because x = -2 is a counterexample. We get: "False if and only if True" which itself is false.

User AvZ
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories