24 votes 24 votes The number of elements in the power set $P(S)$ of the set $S=\{\{\emptyset\}, 1, \{2, 3\}\}$ is: $2$ $4$ $8$ None of the above Set Theory & Algebra gate1995 set-theory&algebra normal set-theory + – Kathleen asked Oct 8, 2014 • recategorized Apr 25, 2021 by Lakshman Bhaiya Kathleen 16.4k views answer comment Share Follow See all 7 Comments See all 7 7 Comments reply Show 4 previous comments BharathiCH commented Dec 22, 2018 reply Follow Share @Abhisek Tiwari 4 Then the elements will be as {∅,{∅},{1},{{2,3}},{∅,1},{1,{2,3}},{∅,{2,3}},{∅,1,{2,3}}}.. Then {∅,1} and {1} are they not equal? 0 votes 0 votes Abhisek Tiwari 4 commented Dec 22, 2018 reply Follow Share @BharathiCH Yes {1} and { {∅},1} different. [Note it should be {{∅},1} instead of {∅,1} 2 votes 2 votes endurance1 commented Mar 3, 2021 reply Follow Share It is explicitly said in the question that what ever S is, it a set according to paper setter, so we just need to calculate the cardinality and apply the formula. 0 votes 0 votes Please log in or register to add a comment.
Best answer 34 votes 34 votes Number of elements in power set $= 2^{\text{(no of elements in the set)}} = 2^{3} = 8$ Elements are $\{∅,\{\{∅\}\},\{1\},\{\{2,3\}\},\{\{∅\},1\},\{1,\{2,3\}\},\{\{∅\},\{2,3\}\},\{\{∅\},1,\{2,3\}\}\}$ Hence, Option is $(C): 8.$ jayendra answered Dec 27, 2014 • edited May 10, 2019 by Arjun jayendra comment Share Follow See 1 comment See all 1 1 comment reply Deepak Poonia commented Apr 23, 2022 reply Follow Share Video Solution 2 votes 2 votes Please log in or register to add a comment.
5 votes 5 votes S={{ϕ},1,{2,3}} cardinality of S= 3 then cardinality of Power set of S = 2^3 =8 Hence ,Option (C)8 is the correct answer. Warrior answered Jul 29, 2017 Warrior comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes Since there are three elements in the set S , so the power of this set P( S)= 2 ^3= 8. Hence the option C is correct. DIBAKAR MAJEE answered Apr 26, 2020 DIBAKAR MAJEE comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes S = {(φ), 1, (2, 3)} P(S) = {φ, {{φ}}, {1}, {{2, 3}}, {{φ}, 1}, {1, {2, 3}}, {{φ}, 1, {2, 3}}} In P(S) it contains 8 elements. varunrajarathnam answered Oct 3, 2020 varunrajarathnam comment Share Follow See all 0 reply Please log in or register to add a comment.