  # Complement of a set

The Set U = { a,b, c,d, e,f,} A= {a, c, e} B= { b, d , e, f,} C= { a,b,d,f] Find each specified set

1.(A U B) U C'
Upside down U for aub i couldn't do it on my keyboard but i am having problems with this question

### Comments for Complement of a set

 Jan 21, 2011 Universal Complement of a Set by: Staff The question: U = {a, b, c, d, e, f} A= {a, c, e} B= {b, d, e, f,} C= {a, b, d, f} Find each specified set (A U B) U C' Upside down U for aub i couldn't do it on my keyboard but i am having problems with this question The answer: To type the following symbols on your keyboard, hold down the ALT key, type the code, then release the ALT key: ⊂, subset, 8834 ⊃, superset, 8835 ∈, element of a set, 8712 ∩, intersection, 8745 ∪, union, 8746 Ø, null set, 0216 As I understand it, this is what you intend your expression to be: (A ∩ B) ∪ C' Step 1: A ∩ B, set A intersection with set B The intersection of A and B is a new set which contains the elements common to both A and B A= {a, c, e} B= {b, d, e, f,} A ∩ B = {e}; e is the only element which appears in both set A and set B Step 2: C' C', set C followed by the prime symbol ' stands for the universal (or absolute) complement of set C. This means EVERYTHING in the universe which is NOT in set C. C = {a, b, d, f} C' = everything in the universe except for {a, b, d, f} Your universal set, U U = {a, b, c, d, e, f} C' = {c, e} Step 3: {e}∪ C', the union of {e} with C' {e}∪ C' The element e already appears in C'. The union of e with C' is still C'. {e}∪ {c, e} = {c, e} The final answer is: (A ∩ B) ∪ C' = C' (A ∩ B) ∪ C' = {c, e} Thanks for writing. Staff www.solving-math-problems.com