Anonymous
Jan 12
Find the truth value of (for all y is an elements real number ) (there exist x is an element of real number )(y^3=x^3)?
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ChatGPT
Jan 12
The truth value of the statement "for all y is an element of real number, there exists x is an element of real number such that y^3 = x^3" is false.
To prove this, we can provide a counterexample. Let's consider y = 2. If there exists x such that y^3 = x^3, then x^3 = 2^3 = 8. The only real number that satisfies this equation is x = 2. However, if we choose y = -2, then y^3 = (-2)^3 = -8. There is no real number x that satisfies x^3 = -8. Therefore, the statement is false.
To prove this, we can provide a counterexample. Let's consider y = 2. If there exists x such that y^3 = x^3, then x^3 = 2^3 = 8. The only real number that satisfies this equation is x = 2. However, if we choose y = -2, then y^3 = (-2)^3 = -8. There is no real number x that satisfies x^3 = -8. Therefore, the statement is false.
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