Question

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.

Answer 1

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Explanation:

True Mathematical Statement

`\text{If }√(x)=a$ and √(y)=b,$ then √(xy)=ab`

False Mathematical Statement

`\text{If }√(x)=a$ and √(y)=b,$ then √(x+y)=a+b`

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

`\text{Let x}=16\\\text{Let y}=9\\√(16)=4\\√(9)=3\\√(16+9)=√(25)=5\\a+b=3+4=7\\5\\eq 7`

Therefore, the mathematical statement is false.