Find the power set of each of these sets, where a and b are distinct elements. a) {a} b) {a, b} c) {1, 2, 3, 4} show steps

a) {{}, {a}}.

b) {{}, {a}, {b}, {a, b}}.

c) {{}, {1}, {2}, {1, 2}, {3}, {1, 3}, {2, 3}, {1, 2, 3}, {4}, {1, 4}, {2, 4}, {1, 2, 4}, {3, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}.

Step-by-step explanation:

The power set of a set is the set of all subset of the set in question. The number of power sets (including the empty set) of a set with (where ) unique elements is .

In other words, there shall be

This explanation shows how to find the power set using binary numbers (only 0 and 1.) (Credit: Mathsisfun.)

List all the binary numbers that are equivalent to decimals ranging from 0 to .

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Reverse the original set. Each digit in the binary number corresponds to a member of the original set (i.e. a letter in a) and b) or a number in c).) 0 means that the element is absent in the subset and 1 means that the element is present.

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The power set of a) thus contains:

Similarly, list all the binary numbers that are equivalent to decimals ranging from 0 to .

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The power set of b) thus contains:

Similarly, list all the binary numbers that are equivalent to decimals ranging from 0 to .

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The power set of c) thus contains:

∞ this is your sign

the answer to the expression is 83