Counting Elements in Sets: Steps Included

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SUMMARY

This discussion focuses on counting the number of elements in specific power sets. The sets in question are P({a,b}), P({∅,a,{a},{{a}}}), and P(P(∅)). The solutions reveal that P({a,b}) contains 4 elements, P({∅,a,{a},{{a}}}) contains 8 elements, and P(P(∅)) contains 2 elements. Each solution is derived from the fundamental principle of power sets, which states that the power set of a set with n elements contains 2^n elements.

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Madonna M.
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How many elements does each of these sets have where a and b are distinct elements? (with steps please)

a) P({a,b{a,b}})b)P({∅,a,{a},{{a}}})
c)P(P(∅))

*i have tried to solve them but i am a little bit confused...

Thanks in advance :)
 
Last edited:
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Pls post your attempts at solution, including any reasoning.
 

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