Answer
No, it does not show that the specified arguments are true.
Work Step by Step
The definition of a valid argument is an argument in which the truth of all the premises forces the truth of the conclusion.
In this example, the two premises can never be true simultaneously, because they are contradictory, irrespective of the true status of the tooth fairy.
Therefore it is (vacuously) true that whenever both of the premises are true, the conclusion is also true (irrespective of your luck at finding gold at the end of the rainbow).
Because the premises are not both true, we cannot conclude that the conclusion is true.
