Question 7: Write down the power set of each of the following sets:
\((ii)\) \(\;\) \(\{+,-, \times, \div\}\)
Solution:
\(\{\)\(\phi,\)\( \{+\}, \)\(\{-\},\)\(\{\times\},\)\(\{\div\},\)\(\{+,-\},\)\(\{+,\times\},\)\(\{+, \div\},\)\(\{-, \times\},\)\(\{-, \div\},\)\(\{\times, \div\},\)\(\{+,-,\times\},\)\(\{+,-,\div\},\)\(\{+,\times, \div\},\)\(\{-,\times, \div\},\)\(\{+,-,\times, \div\}\)\(\}\)
Explanation:
A power set is the set of all possible subsets of a given set.
That includes:
- The empty set
- Each element by itself
- Any combinations of elements
- The full set itself
The set should contain \(2^4=16\) elements.