Theory question 101
Algebraic Expressions(a) Factorize: px − 2qx − 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∪Q]' = P'∩Q'.
Show the model answer
Model answer
(a) Group: x(p − 2q) + 2y(p − 2q) = (p − 2q)(x + 2y)
(b) P∪Q = {1, 2, 3, 4, 6, 9, 10}, so (P∪Q)' = {5, 7, 8}
P' = {3, 5, 7, 8, 9}, Q' = {1, 4, 5, 7, 8, 10}, so P'∩Q' = {5, 7, 8}
Both sets are {5, 7, 8}, so (P∪Q)' = P'∩Q'
Explanation
Group the terms in pairs that share a common factor.