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Proofs are used to show that a mathematical statement is true. The most common form of mathematical statements are if-then statements. Give an example of a true mathematical statement and a false mathematical statement in if-then form. For the false statement, include a counterexample showing that the statement isn't true.

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Step-by-step explanation:

True Mathematical Statement

[tex]\text{If }\sqrt{x}=a$ and \sqrt{y}=b,$ then \sqrt{xy}=ab[/tex]

False Mathematical Statement

[tex]\text{If }\sqrt{x}=a$ and \sqrt{y}=b,$ then \sqrt{x+y}=a+b[/tex]

To show using a counterexample that the statement isn't true.

[tex]\text{Let x}=16\\\text{Let y}=9\\\sqrt{16}=4\\\sqrt{9}=3\\\sqrt{16+9}=\sqrt{25}=5\\a+b=3+4=7\\5\neq 7[/tex]

Therefore, the mathematical statement is false.

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