For a set π΄, the power set of π΄ is denoted by 2π΄. If π΄ = {5,{6},{7}},β¦
2015
For a set π΄, the power set of π΄ is denoted by 2π΄. If π΄ = {5,{6},{7}}, which of the following options are TRUE?
I. β β 2π΄
II. β βΒ 2π΄
III. {5,{6}} βΒ 2π΄
IV. {5,{6}} β 2π΄
- A.
I and III only
- B.
II and III only
- C.
I, II and III only
- D.
I, II and IV only
Attempted by 578 students.
Show answer & explanation
Correct answer: C
Key idea: the power set 2A consists of all subsets of A.
β β 2A because the empty set is a subset of every set (so it is one of the subsets of A).
β β 2A because the empty set is a subset of every set.
{5,{6}} β 2A because {5,{6}} is a subset of A (both 5 and {6} are elements of A), so that subset is one element of the power set.
{5,{6}} β 2A is false because its elements (5 and {6}) are not subsets of A and therefore are not elements of 2A.
Conclusion: I, II and III are true; IV is false. So the correct selection is I, II and III only.
A video solution is available for this question β log in and enroll to watch it.