Consider a statement of the form x S st Px True or False Are

Consider a statement of the form: x S, s.t. P(x) True or False: Are the following valid ways to prove the above statement? Enter T if it is a valid approach, F if it is not valid. Find specific values of x for which ~ P(x) is false. Find specific values of x for which P(x) is true. Show that one can construct a value of x S with the desired property P(x) Prove that the statement x S, ~ P(x) is false. Show that if there does not exist an x S with the desired property, then there is a contradiction to a previously established result or theorem

Solution

1. False

2. True

3. True

4. False

5.True