First Order Logic

Question

Consider the following statements in first-order logic:

S1 : [∃xP(x) ∧ ∃x{P(x) → Q(x)}] → ∃xQ(x)
S2 : [∀xP(x) ∧ ∀x{P(x) → Q(x)}] → ∃xQ(x)
S3 : {∀xP(x) ∧ ∃xQ(x)} → ∃x{P(x) ∧ Q(x)}

Which of the following is true?

Answer 1

s3 will be correct....the if inference rules and rules of universal and existential specialization and generalisation are applied will result in false ....in s3 if we try to make right hand side false left hand side will be false annd thus overall becomes true