What is wrong with the given proof to prove the following theorem? Theorem: If x

Question

What is wrong with the given proof to prove the following theorem? Theorem: If x is a real number, then x^2 is a positive real number. Proof: Let p_1 be "x is positive." statement. Let p_2 be "x is negative." statement, and let q be "x^2 is positive." statement. To show that p_1 rightarrow q is true, note that when x is positive, x^2 is positive because it is the product of two positive numbers, x and x. To show that p_2 rightarrow q, note that when x is negative, x^2 is positive because it is the product of two negative numbers, x and x. This completes the proof.

Explanation / Answer

The problem with the proof is that it does'nt consider the case of 0 which is a non-negative , non-positive real number and it's square is 0 which is not positive .

The proof as part of the problem statement is for the Theorem :

If x is a positive or negative real number , then x2 is positive .

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