Formula to find the number of subsets of a set that has "n" number of elements. 2 raise 1)to the nth power 2)n squared 3)2 times
1 answer:
Answer:
(A)
Step-by-step explanation:
Given a set with "n" number of elements, the collection of all subsets of the set is referred to as the Power set of the given set.
To find the number of possible subsets of any set, we use the formula:
Take for example the set: A={2,3,4)
A has 3 elements, therefore n=3
The number of possible subsets of A is:
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Answer: The number is: " 12 ".
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Let "x" represent "the unknown number" (for which we wish to solve.
The expression:
x <span>− 6 = 2 ; Solve for "x" ;
</span>_______________________________________________
Method 1)
Add "6" to EACH SIDE of the equation;
_______________________________________________
→ x − 6 + 6 = 2 + 6 ;
to get:
→ x = 8 ;
______________________________________________
Multiply each side of the equation by "
" ; to isolate "x" on one side of the equation ; and to solve for "x" ;
______________________________________________
→ * x = 8 * ;
→ x = 8 * ;
=
* ;
=
;
=
;
= <span>1<span>2 .</span></span>
______________________________________________
x = 12 .
______________________________________________
Method 2)
______________________________________________
x − 6 = 2 ; Solve for "x" ;
Add "6" to EACH SIDE of the equation;
_______________________________________________
→ x − 6 + 6 = 2 + 6 ;
to get:
→ x = 8 ;
______________________________________________
Multiply each side of the equation by "3" ; to get rid of the "fraction" ;
→ 3 * x = 8 * 3 ;
→
* x = 8 * 3 ;
→
x = 8 * 3
→
x = 24 ;
→ 2x = 24 ;
→ Divide each side of the equation by "2" ; to isolate "x" on one side of the equation; & to solve for "x" :
2x / 2 = 24 / 2 ;
x = 12 .
__________________________________________________
Method 3).
__________________________________________________
x − 6 = 2 ; Solve for "x" ;
_______________________________________________
Add "6" to EACH SIDE of the equation;
_______________________________________________
→ x − 6 + 6 = 2 + 6 ;
to get:
→ x = 8 ;
______________________________________________
Now, divide each side of the equation by " " ;
to isolate "x" on one side of the equation; & to solve for "x" ;
___________________________________________________
{ x } / {} = 8 / {} ;
to get: x = 8 / {} ;
= 8 * ( ;
=
* 
;
= ;
= ;
= 12 ;
___________________________________________
x = 12 .
___________________________________________
NOTE: Variant: (in "Methods 2 & 3") :
___________________________________________
At the point where:
___________________________________________
= 8 * () ;
= * ;
__________________________________________
We can cancel out the "2" to a "1" ; and we can cancel out the "8" to a "4" ;
__________________________________________
{since: "8÷2 = 4" ; and since: "2÷2 =1" } ;
__________________________________________
and we can rewrite the expression:
__________________________________________
* ;
__________________________________________
as:
* 
;
__________________________________________
which equals:
__________________________________________
→
;
=
;
= 12 .
__________________________________________
x = 12 .
__________________________________________
Answer: The number is: " 12 ".
__________________________________________
____________________________________
Let "x" represent "the unknown number" (for which we wish to solve.
The expression:
</span>_______________________________________________
Method 1)
Add "6" to EACH SIDE of the equation;
_______________________________________________
→
to get:
→
______________________________________________
Multiply each side of the equation by "
______________________________________________
→
→ x = 8 *
=
=
=
= <span>1<span>2 .</span></span>
______________________________________________
x = 12 .
______________________________________________
Method 2)
______________________________________________
Add "6" to EACH SIDE of the equation;
_______________________________________________
→
to get:
→
______________________________________________
Multiply each side of the equation by "3" ; to get rid of the "fraction" ;
→ 3 *
→
→
→
→ 2x = 24 ;
→ Divide each side of the equation by "2" ; to isolate "x" on one side of the equation; & to solve for "x" :
2x / 2 = 24 / 2 ;
x = 12 .
__________________________________________________
Method 3).
__________________________________________________
_______________________________________________
Add "6" to EACH SIDE of the equation;
_______________________________________________
→
to get:
→
______________________________________________
Now, divide each side of the equation by "
to isolate "x" on one side of the equation; & to solve for "x" ;
___________________________________________________
{
to get: x = 8 / {
= 8 * (
=
=
=
= 12 ;
___________________________________________
x = 12 .
___________________________________________
NOTE: Variant: (in "Methods 2 & 3") :
___________________________________________
At the point where:
___________________________________________
= 8 * (
=
__________________________________________
We can cancel out the "2" to a "1" ; and we can cancel out the "8" to a "4" ;
__________________________________________
{since: "8÷2 = 4" ; and since: "2÷2 =1" } ;
__________________________________________
and we can rewrite the expression:
__________________________________________
__________________________________________
as:
__________________________________________
which equals:
__________________________________________
→
=
= 12 .
__________________________________________
x = 12 .
__________________________________________
Answer: The number is: " 12 ".
__________________________________________