set-builder notation: {x ɛ Z| x = x^2 for int. y ≤ 3}, {x ɛ Z| x^2 = y w/ int. y ≤ 3}

[Fares]

set-builder notation: {x ɛ Z| x = x^2 for int. y ≤ 3}, {x ɛ Z| x^2 = y w/ int. y ≤ 3}

Hi guys this is my first post i hope you help me as soon as possible
i got these two questions which are due next sunday

(a) {x ɛ Z| x = x^2 for some integer y ≤ 3}
(b) {x ɛ Z| x^2 = y for some integer y ≤ 3}

so in (b) i think the answer is {-1, 0, 1} because y can only be equal to a positive integer which is less than or equal to 3 that only applies when x is equal to one of the previously mentioned integers.

but in (a) i think there is a typo as it should be x ≤ 3 instead of y ≤ 3. If so, the answer is probably {0, 1}.

thanks in advance...

 

[ksdhart2]

Hi guys this is my first post i hope you help me as soon as possible
i got these two questions which are due next sunday

(a) {x ɛ Z| x = x^2 for some integer y ≤ 3}
(b) {x ɛ Z| x^2 = y for some integer y ≤ 3}

so in (b) i think the answer is {-1, 0, 1} because y can only be equal to a positive integer which is less than or equal to 3 that only applies when x is equal to one of the previously mentioned integers.

but in (a) i think there is a typo as it should be x ≤ 3 instead of y ≤ 3. If so, the answer is probably {0, 1}.

thanks in advance...

I suspect you're correct that there is a typo in part (a), but it doesn't actually change the answer. Interestingly enough, imposing the condition x <= 3 doesn't change the answer either. You're tasked with finding the solutions to the equation x = x². This can be reformulated as finding the roots of the polynomial x² - x = 0. By the Fundamental Theorem of Algebrahttps://www.mathsisfun.com/algebra/fundamental-theorem-algebra.html, this degree-two polynomial is guaranteed to have exactly 2 roots. You've correctly identified that these roots are x = 0 and x = 1. There's no y anywhere in the problem text for part (a), so this must hold for any value of y.