JEE Main202126 Feb 2021Evening ShiftMathematicsMathematical ReasoningActual
Let F 1 A , B , C = A ∧ ~ B ∨ ~ C ∧ A ∨ B ∨ ~ A and F 2 A , B = A ∨ B ∨ B → ~ A be two logical expressions. Then :
Options
- AF 1 is a tautology but F 2 is not a tautology
- BF 1 is not a tautology but F 2 is a tautology
- CBoth F 1 and F 2 are not tautologies
- DF 1 and F 2 both are tautologies
Correct answer
B. F 1 is not a tautology but F 2 is a tautology
Step-by-step solution
F 1 : A ∧ ~ B ∨ ~ C ∧ A ∨ B ∨ ~ A F 2 : A ∨ B ∨ B → ~ A F 1 : A ∧ ~ B ∨ ~ A ∨ A ∨ B ∧ ~ C : A ∨ ~ A ∧ ~ A ∨ ~ B ∨ A ∨ B ∧ ~ C : t ∧ ~ A ∨ ~ B ∨ A ∨ B ∧ ~ C : ~ A ∨ ~ B ∨ A ∨ B ∧ ~ C : ~ A ∨ ~ B ∨ A ∨ B ⏟ t ∧ ~ A ∨ ~ B ∧ ~ C F 1 : ~ A ∨ ~ B ∧ ~ C ≠ t (tautology) F 2 : A ∨ B ∨ ~ B