<p>If x = y, then x^2 = y^2
If x and y are real numbers, which of the following CANNOT be inferred from the statement above?</p>
<p>a) in order for x^2 to be equal to y^2, it is sufficient that x be equal to y
b) a necessary condition for x to be equal to y is that x^2 be equal to y^2
c) x is equal to y implies that x^2 is equal to y^2
d) if x^2 is not equal to y^2, then x is not equal to y
e) if x^2 is equal to y^2, then x is equal to y</p>
<p>This is a math question, already posted on CC, but I didn't want to revive an old thread. So, my question is why is B wrong?</p>
<p>The way I understand it is that B says: If x^2 = y^2, then x = y (x^2 = y^2 is the (necessary) condition).</p>
<p>If x^2 = y^2, x does not necessarily = y because x= -2 and y= 2 is a counterexample.</p>
<p>What’s the answer? Is it E?</p>
<p>Yes, it seems to be E. B is right because if x=y, then x^2 must equal y^2. Thus, x^2 = y^2 is a necessary condition for x=y. OP, your interpretation of B is wrong because your interpretation is exactly what E says (the correct answer).</p>
<p>This question seems similar a college board question but not quite right. Where is it from? As it is written, it is logically flawed since it asks you which of the following cannot be inferred from a given statement, but the given statement is itself false. Also, the given statement is unnecessary.</p>
<p>They could have worded it:“If x and y are real numbers, which of the following is false?”</p>
<p>That would at least be logical. The way they have it worded now actually makes no sense. Can’t be a real SAT question…</p>
<p>
The statement is true. If x = y, then x^2 = y^2. I challenge you to provide a counterexample to this statement.</p>
<p>Hello, hello…is this thing on? Something is locked. Is it my keyboard? Nope, my brain…</p>
<p>Sorry, all. :)</p>
<p>But the problem still seems funny in that the statement is superfluous. The answer choices are true or false on their own merit, not because they can or cannot be inferred from the given statement. So, my brain lock aside, it still seems like a bogus question to me.</p>
<p>Pckeller, this is a Math II question from CB. Probably it’s not the type of SAT I Math questions you’re exposed to, but I believe this one’s an official question.</p>
<p>93tiger166. So, the condition in a conditional statement is actually the conclusion? I.e In “if x = y, then x^2 = y^2”, the condition is x^2 = y^2 ?</p>
<p>I’m confused. The answer says that “b) a necessary condition for x to be equal to y is that x^2 be equal to y^2.” Doesn’t that mean that for x to be equal to y, x^2 needs to be equal to y^2? This is false, because x can equal 2, and y can equal -2. So why isn’t B the answer? I understand that E says the same thing, but just making sure I’m not reading it wrong.</p>
<p>B is basically saying that if x = y then x^2 must equal y^2, which is true.</p>
<p>ccuser, that is not a conditional statement; it is a fact. There are no conditional limitations; that is, it works in all cases. If x = y, then x^2 must equal y^2. No counter examples exist.</p>
<p>omnipotent, for x to equal y, x^2 must equal y^2. That CAN be inferred from the given statement; in fact, it’s just the converse of the statement for some of the cases. It does NOT say that x HAS to equal y if their squares equal each other. That is, for the mere POSSIBILITY of x equaling y, their squares have to be equal. Because, if their squares aren’t equal, you cannot possibly get x to equal y. That’s why B is true.</p>
<p>So I got this from Wikipedia:</p>
<p>Example 1: In order for it to be true that “John is a bachelor,” it is necessary that it be also true that he is
unmarried
male
adult</p>
<p>Now, I think I can see that the “necessary condition” x^2 = y^2 is not a prerequisite for x to equal y, but only one of the possible many conditions. Therefore it does not suffice to conclude from the condition x^2 = y^2 that x=y, but only from x=y can you conclude x^2=y^2. E.g only from the fact that john is a bachelor can we conclude that he is an adult. Thus, if John is a bachelor, he is an adult, and not the other way around. So, back to our case, Choice B reads: if x = y, then x^2 = y^2.
It was counter-intuitive at first, before thinking of many conditions.</p>
<p>Here’s another example:
Being at least 30 years old is necessary for serving in the U.S. Senate.</p>
<p>Thus, we can’t say that if you’re 30 years old, you’re serving in the US Senate. Here, we have a “necessary” condition. What we can say is this: If you’re serving in the US Senate, then you are at least 30 years old.</p>
<p>To generalize on the above information, and make it more formulaic, I devised this:</p>
<p>If x, then y => y is a necessary condition for x (or x cannot occur without y)
If x, then y => x is sufficient for y
If x, then y => x implies y.</p>