Q55MCQ2 marks, −0.67Which one of the following well-formed formulae is a tautology?(A)∀x ∃y R(x,y) ↔ ∃y ∀x R(x,y)\forall x \, \exists y \, R(x,y) \, \leftrightarrow \, \exists y \, \forall x \, R(x, y)∀x∃yR(x,y)↔∃y∀xR(x,y)(B)(∀x [∃y R(x,y) → S(x,y)]) → ∀x ∃y S(x,y)( \forall x \, [\exists y \, R(x,y) \, \rightarrow \, S(x, y)]) \, \rightarrow \, \forall x \, \exists y \, S(x, y)(∀x[∃yR(x,y)→S(x,y)])→∀x∃yS(x,y)(C)[∀x ∃y (P(x,y) → R(x,y))] ↔[∀x ∃y(¬P(x,y) ∨R(x,y))][ \forall x \, \exists y \, \left( P(x,y) \, \rightarrow \, R(x, y) \right)] \, \leftrightarrow [ \forall x \, \exists y \left(\neg P(x, y) \, \lor R(x, y) \right)][∀x∃y(P(x,y)→R(x,y))]↔[∀x∃y(¬P(x,y)∨R(x,y))](D)∀x ∀y P(x,y) → ∀x ∀y P(y,x)\forall x \, \forall y \, P(x,y) \, \rightarrow \, \forall x \, \forall y \, P(y, x)∀x∀yP(x,y)→∀x∀yP(y,x)Sign in to save attempts.Show answer← PreviousSolutionsDiscussionLoading…Sign in with Google