III BA, B.Sc. Mathematics Paper IV (Elective-2) - Acharya Nagarjuna ...

III B.A./B.Sc. Mathematics12Paper IV (Elective -2) - Curriculum15.(a) In any Boolean algebra, if a∧ x = a∧ yand a∨ x = a∨ y, then prove that x = y.'(b) Write the gating network representing the boolean expression [ ]( x1∨x2) ∧x3 ∨( x1∧ x2).OR16.(a) If any Boolean algebra B = [ A , ∧, ∨, '], prove that the relation a< b is a partial ordering of A.Moreover, in terms of this partial ordering, prove that a∧ b = glb { ab , } and a∨ b = lub { ab , }.(b) Show that ( p→q) →[( r∨ p) →( r∨ q)]is a tautology , regardless of r .Y