Now the proposition is symbolized, and the individual domain is regarded as the total individual domain.

R (x): x is a real number; N (x): x is a natural number, and z (x): x is an integer.

Premise: Ex(R(x)∧N(x)), Ax(N(x)→Z(x)).

Conclusion: Ex(R(x)∧Z(x)).

Prove:

① Ex(R(x)∧N(x)) *****

② R(a)∧N(a) ******

③ Not applicable.

④ Ax(N(x)→Z(x))

⑤ N(a)→Z(a)

⑥ Z(a)

⑦ R(a)

⑧ R(a)∧Z(a)

⑨ Ex(R(x)∧Z(x))

Get a license.

Note: I leave the reasons behind each sentence to you.