Universe is set of all mobiles. Here, M(x) is true for all x.
Option A : Only mobiles are black ≡ If x is not mobile then x is not black ≡ If x is black then x is mobile ≡ True.
∀x ( M(x) → X(x) ) ≡ ∀x ( T → B(x) ) ≡ ∀x ( B(x) ).
Statement doesn’t match expression.Thus, not correct.
Option B : Only mobiles are black ≡ If x is not mobile then x is not black ≡ If x is black then x is mobile ≡ True.
∀x ( M(x) v B(x) ) ≡ ∀x ( T v B(x) ) ≡ True.
Statement matches expression.Thus, correct pair.
Option C : All and Only black mobiles have calculator ≡ All blacks have calculator and only blacks have calculator ≡ If x is black then x have calculator and if x have calculator then x is black.
∀x ((C(x) ^ M(x)) ↔ B(x)) ≡ ∀x (( C(x) T) ↔ B(x)) ≡ ∀x (C(x) ↔ B(x))
≡ ∀x ( (B(x) → C(x)) ^ (C(x) → B(x) ).
Statement matches expression.Thus, correct pair.
Option D : All mobiles have calculator ≡ All x have calculator.
∀x ( M(x) ^ C(x) ) ≡ ∀x ( T ^ C(x) ) ≡ ∀x ( C(x) ).
Statement matches expression.Thus, correct pair.
Answer:- B, C, D.