(a) Factorise : (px – 2px – 4qy + 2py)
(b) Given that the universal set U = {1, 2, 3, 4,5, 6, 7, 8, 9, 10}, P = {1, 2, 4, 6, 10} and Q = {2, 3, 6, 9}; show that ((P cup Q)’ = P’ cap Q’)
Explanation
(a) (px – 2qx – 4qy + 2py)
= (x(p – 2q) + 2y(p – 2q))
= ((x + 2y)(p – 2q))
(b) (U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10})
(P = {1, 2, 4, 6, 10} ; Q = {2, 3, 6, 9})
((P cup Q) = {1, 2, 3, 4, 6, 9, 10})
((P cup Q)’ = {5, 7, 8})
(P’ cap Q’ = {3, 5, 7, 8, 9} cap {1, 4, 5, 7, 8, 10})
= ({5, 7, 8})
Hence, ((P cup Q)’ = P’ cap Q’).