Let R be the statement "x^3 +32 = 5 for all real numbers x such that x^2 +32 = 0"
Is R true? Why or why not?
To me, this says that x must be real and must satisfy both equations. Since there is no real x that satisfies the second equation, the entire statement must be false. The only problem is, I have no idea if I'm interpreting the statement correctly.
It also seems like one could read this as "the set of solutions for the second equation must be contained within the set of solutions for the first equation". And since the empty set is contained within all sets (including x=-3), then the statement would be true.
First week of my proofs class and I'm already stumped. Any help?