posted by .

If A is a finite set and B is a proper subset of A, prove that |B| < |A|.
Hint: B is finite. What is the union of the disjoint sets B and A - B?

Note: |A| = size of A

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    what is the property that distinguishes finite sets from infinite sets (give examples of each to accompany explaination). finite sets are countable. Infinite sets are not. so what would be an example of an infinite set?
  2. math

    Prove that the union of two finite sets is finite. Hint: A U B = (A - B) U (B - A) U (A ∩ B) where U = union and ∩ = intersection
  3. smallest algebra

    Let F be a family of subsets of a set X such that empty set is the element of F. A subset A of X belongs to F1 if and only if either A is a subset of F or complement of A is the subset of F. A subset B of X belongs to F2 if and only …
  4. Set Theory

    Given the sets A=[a,b], B=[a,b,c], C=[b,c,d] Prove that if A is a subset of B and B is a subset of C then A is a subset of C
  5. Set Thoery

    (1)Given the sets A={a,b}, B={a,b,c}, C= {b,c,d}. which of these sets are: (i) Equal (ii) Comparable (iii) Subset (2) Prove that if A is a subset of B and B is a subset of C then A is a subset of C
  6. Algebra

    Observe the following sets and answer he quesions given below. A = The set of all residens in Mumbai. B = he set of all residens in Bhopal. C = he sets of all residents in Maharashtra. D = The sets of all residents in India. E = The …
  7. math

    Let f:A->B, where A and B are nonempty, and let T1 and T2 be subsets of B. a.Prove that f^-1(T1 U T2)= f^-1(T1) U f^-1(T2). b.Prove that f^-1(T1 intersects T2) = f^-1(T1) intersects f^-1(T2). I think once I see a I can do b. c. …
  8. Finite Math

    Sizes of disjoint subsets of a universal set. Assume that A and B are disjoint subsets of U, and that n(U)=95, n(A)=30,and n(B')=61. Find n(A¿B').
  9. Discrete Math

    For sets A, B, C is a subset of U, prove or disprove (with a counter-example) the following: If A is a subset of B, B is not a subset of C, then A is not a subset of C,
  10. math

    Define A relation S for subset of R by S=[{A,B:ACR,B is improper Subset to R,[A/B]u[B/A]is finite prove that s is an equivalent relation and the family of finite subset of R one equivalent class

More Similar Questions