Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Universal set (U): is a set U, which contains all the sets under consideration as a subsets of U.
e.g.: For the set B of all integers, the universal set can be a set of all real numbers. It can also be a set of all rational numbers.

Complement of set: Let U be the universal set and A is a subset of U. Then the complement of A (written as A')is a set of all elements of U which doesnâ€™t belong to A.
A' = {x: x â‚¬ U and x not â‚¬ A}

Union of sets: C = A U B = {x: x â‚¬ A or x â‚¬ B}.
e.g.: For the set B of all integers, the universal set can be a set of all real numbers. It can also be a set of all rational numbers.

Intersection of sets: C = A Π B = {x: x â‚¬ A and x â‚¬ B}.
Disjoint sets: if A Π B = Φ, then A and B are Disjoint sets.
e.g.: A={2,4,6,8} and B={1,2,6}, then A Π B = {2,6}

Difference of sets: A â€“ B = {x: x â‚¬ A and x â‚¬ B}
e.g.: A = {a,e,i,o,u} and B = {a,i,o,k}. Then A â€“ B = {e,u} and B â€“ A = {k}. Hence, A â€“ B not equal to B - A

If a set has 6 elements, the number of subsets is 12. correct?

If a set has n elements, number of subsets = 2^n

why?

How did you get 12 subsets for 6 elements?

Note that you ought to consider null set and the set itself as the subsets.
Let me give you an example of a set with 3 elements S = {a,b,c}
Subsets:
null set
S
{a}
{b}
{c}
{a,b}
{b,c}
{a,c}

If a set has 6 elements, the number of subsets is 12. correct?

If a set has n elements, number of subsets = 2^n

why?

How did you get 12 subsets for 6 elements? Note that you ought to consider null set and the set itself as the subsets. Let me give you an example of a set with 3 elements S = {a,b,c} Subsets: null set S {a} {b} {c} {a,b} {b,c} {a,c}

thanks for the explanation. i was reading someone's math notes i got off the internet. i questioned this concept but i was too tired to think it out. i guess he apparently forgot the caret, which is immensely important to the meaning of the "equation"