Question

find the power set of the following sets: B{1, 2, 3}. C{p, q, r, s}​

Answer 1

1) The subsets of B are ϕ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3} The power set of B

P(B) = {Ø, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3}}

2) Set :- A collection of well defined objects. A set may have infinite or finite objects .Every object is called element of the set.

Subset :- It is the set of few or all elements of a set.

Power set :- It is the set of all subsets of the set including itself and the empty set.

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Power set is the set of all possible sets.

D = { p, q, r, s }

P ( D) = { p, q, r, s, ( p, q) , ( q, r) , ( r, s) , ( s, p) , ( p , r) , ( q, s) , ( p, q, r) , ( q, r, s) , ( p, r, s) , ( p, q, s) , ( p, q, r, s), Ø }

The number of elements in set n ( D) = 4

Number of elements in power set n(P ( D) ) =

${2}^{n(d)}$

Therefore, Number of elements in power set = 2^4 = 16 .

Answer 2

Step-by-step explanation:

$1) The subsets of B are ϕ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3} The power set of B</p><p>P(B) = {Ø, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3}}</p><p>2) Set :- A collection of well defined objects. A set may have infinite or finite objects .Every object is called element of the set.</p><p>Subset :- It is the set of few or all elements of a set.</p><p>Power set :- It is the set of all subsets of the set including itself and the empty set.</p><p>=======================================</p><p>Power set is the set of all possible sets.</p><p>D = { p, q, r, s }</p><p>P ( D) = { p, q, r, s, ( p, q) , ( q, r) , ( r, s) , ( s, p) , ( p , r) , ( q, s) , ( p, q, r) , ( q, r, s) , ( p, r, s) , ( p, q, s) , ( p, q, r, s), Ø }</p><p>The number of elements in set n ( D) = 4</p><p>Number of elements in power set n(P ( D) ) =</p><p>{2}^{n(d)}2n(d)</p><p>Therefore, Number of elements in power set = 2^4 = 16 .</p><p>$