Question

What is the correct translation of the following statement into mathematical logic?

 "Some real numbers are rational" 

(A) Ǝ x (real(x) v rational (x)) 

(B) ∀x (real (x) →rational (x))

(C) Ǝx (real (x) ∧ rational (x))

(D) Ǝx (rational (x) → Heal (x)}

Answer 1

(C) Ǝ x(real (x) A rational (x))

Option A: There exists x which is either rea l or rational and can be both . 

Option B: All real numbers are rational 

Option C: There exists a real number which is rational. 

Option D: There exists some number which is not rational or which is real.