Question

Ok, I need help with this:

Can the statement be written as a true biconditional statement?

If x = 5, then x^2 =25.


What is a biconditional statement? I don't get it.

Answer 1

A biconditional statement is something of the form

If P, then Q AND if Q then P

So this is essentially saying that P and Q are the same thing

So are the statements x = 5 and x^2=25 the same statement?

Answer 2

Yes, they are in the same statement. And....yeah....they are.

Answer 3

not quite, they look the same, but we need to really check

Answer 4

let's start with the first part: If P then Q

So start with x = 5 and square both sides to get x^2 = 5^2 ---> x^2 = 25

So we've shown that if x = 5, then x^2 = 25. So that part works

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Now let's check: If Q then P

So start with x^2 = 25 and take the square root of both sides to get x = 5 or x = -5 (remember the plus/minus when it comes to solving quadratics). But now we have the extra statement of x = -5, which is nowhere in the first statement. So this means that x^2 = 25 does NOT imply x = 5 alone


So this part does not work


Therefore, the two statements are NOT equivalent

Answer 5

x=5
x^2=25
5^2=5*5
5*5=25
Isn't it right? Or am I missing something?

Answer 6

If however, you wrote the first statement as | x | = 5, then the two would be equivalent

Notice the difference now is that the x is surrounded by absolute value bars

Answer 7

Yes but (-5)^2 = (-5)*(-5) = 25 as well

Answer 8

Ok, thank you jim :)