Question

(a) If A and B given below are two sub-sets of universal sets of natural number ranging from 2 to 16.
A = {6,7,8,9,10,11,12,13,15}
B = {2,4,6,8,10,12,14}
Find:
Complement of A i.e AC
A complement union B complement i.e AC∪ BC

Answer 1

Answer on Question #51645 – Math – Set Theory

(a) If A and B given below are two subsets of universal sets of natural number ranging from 2 to 16.

A = {6,7,8,9,10,11,12,13,15}

B = {2,4,6,8,10,12,14}

Find:

Complement of A i.e AC

A complement union B complement i.e AC ∪ BC

Solution

If A = {6,7,8,9,10,11,12,13,15} and universal set is U={2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}, then Complement of A with respect to U is the set of elements in U but not in A:

$$A ^ {C} = \left\{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 \right\} \setminus \left\{6, 7, 8, 9, 10, 11, 12, 13, 15 \right\} = \left\{2, 3, 4, 5, 14, 16 \right\},$$ $$A ^ {C} = \{2, 3, 4, 5, 14, 16 \}$$ $$B ^ {C} = \{3, 5, 7, 9, 11, 13, 15 \}$$ $$A ^ {C} \cup B ^ {C} = \{2, 3, 4, 5, 7, 9, 11, 13, 14, 15, 16 \}$$

is A complement union B complement.

The union of two sets D and E is the set of elements which are in D, in E, or in both D and E.

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