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2 years ago

Determine the number of subsets and list down all of them.

Mathematics

2 answers:

Setler [38]2 years ago

7 0

We have to use Powerset .All of the elements are subsets of the set.

If n(A)=n

$\boxed{\sf P(A)=2^n}$

{a,b,c}
It has 2^3=8subsets

Now

P(A)={{a},{b},{c},{a,b},{a,c},{b,c},{a,b,c}}

{2,4,6,8}
It has 2^4=16 subsets

Now

P(A)={{2},{4},{6},{8},{2,4},{2,8},{2,8},{4,8},{4,6},{6,8},{2,4,6},{2,4,8},{2,6,8},{4,6,8},{2,4,6,8}}

It has 2^5=32 subsets

Now

P(A)={{1},{2},{3},{4},{5},{1,2},{1,3},{1,4},{1,5},{2,3},{2,4},{2,5},{3,4},{3,5},{4,5},{1,2,3},{1,2,4},{1,2,5}...{1,2,3,4,5}}

Sauron [17]2 years ago

5 0

<h2>✏️ SUBSETS </h2>

$\purple{\underline {\bold{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}}$

$\bold \purple{PROBLEM:}$

Determine the number of subsets and list down all of them.

» 1. { a,b,c }
» 2.{ 2,4,6,8 }
» 3.{ 1,2,3,4,5,}
» 4.{d,e,f,g,h,i}

$\bold \purple{FORMULA:}$

$\underline{ \boxed{ \green{ \rm{ \wp = 2^{n}}}}}$

$\bold \purple{ANSWER:}$

$» \rm \: {1.) \: { a,b,c }}$

$\rm{ \wp = 2^{3} = \green{\boxed{8}}}$

{},{a},{b},{c},{a,b},{a,c},{b,c},{a,b,c}

$» \rm \: {2.)\: { 2,4,6,8 }}$

$\rm{ \wp = 2^{4} = \green{\boxed{16}}}$

{},{2},{4},{6},{8},{2,4},{2,8},{2,8},{4,8},{4,6},{6,8},{2,4,6},{2,4,8},{2,6,8},{4,6,8},{2,4,6,8}

$» \rm \: {3. )\: { 1,2,3,4,5 }}$

$\rm{ \wp = 2^{5} = \green{\boxed{32}}}$

{1},{2},{3},{4,}{5},{1,2},{1,3},{1,4},{1,5},{1,2,3},{1,2,4},{1,2,5},{1,3,4},{1,3,5},{1,4,5},{1,2,3,4},{1,2,3,5},{1,2,4,5},{1,3,4,5},{1,2,3,4,5},{2,3},{2,4},{2,5},{2,3,4},{2,3,5},{2,4,5},{2,3,4,5},{3,4}{3,5}{3,4,5}{4,5},{1,2,3,4,5}.

$» \rm \: {4. )\: { d,e,f,g,h,i }}$

$\rm{ \wp = 2^{6} = \green{\boxed{64}}}$

{d},{e},{f},{g},{h},{i},{d,e},{d,f},{d,g},{d,h},{d,i},{ e,f },{ e,g },{ e,h },{ e,i },{ f,g },{f,h },{ f,i },{ g,h},{ g,i },{ h,i },{ d,e,f },{ d,e,g },{d,e,h },{ d,e,i },{ d,f,g },{ d,f,h },{ d,f,i },{d,g,h },{ d,g,i },{ d,h,i },{ e,f,g },{ e,f,h },{e,f,i },{e,g,h },{ e,g,i },{ e,h,i },{ f,g,h },{ f,g,i },{g,h,i },{d,e,f,g },{d,e,f,h},{ d,e,f,i },{ d,f,g,h },{d,f,g,i},{d,g,h,i},{e,f,g,h},{e,f,g,i},{f,g,h,i},{d,e,f,g,h},{d,e,f,g,i},{e,f,g,h,i},{d,e,f,g,h,i}.

＼(^.^＼)

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Similarly we can check that in the year 1987 the worker earned $$10,500(1.06)^3$ , which makes the pattern clear.

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