MTE 210: Section 2-2

Draw a venn diagram showing the members of congress in the US, the members of the Senate, and the members of the house of representatives.

Square with an S inside and a circle labeled R. U=members of congress, R=members of house. ANSWER: S = R w/a line on top

A third grader asked his teacher whether finite sets could be compared. How do you respond?

Yes and no. They can be compared, they might be equivalent, but not all.

Rewrite the following using mathematical symbols The set consisting of the elements 1 and 2 is a proper subset of ( 1, 2, 3 ).

( 1, 2 ) c ( 1, 2, 3 )

Which of the following represent equal sets?

A = C E = H I = L

Explain why (Ø) has Ø as an element and also a subset.

Since there aren't braces around Ø, it is not in its own box. So it can be both one element and a subset.

How many one to one correspondences are there between 2 sets with... a. 6 elements each? b. n elements each? Explain.

a. 1x2x3x4x5x6= 720 correspondences b. n ( n-1 )( n-2 )... 3x2x1 = n! The first element can be paired with n choices, leaving n-1 elements for the second, pairing and so forth. The fundamental counting theorem says that choices can be multiplied to find the total number of correspondences.

Suppose B is a proper subset of C. a. If n (C) = 8, What is the max # of elements in B? b. If n (B) = 8, what is the max # of elements in C?

a. 8 - 1 = 7max of element in B. b. There is no limit

Find an infinite set such that a. A is finite b. A is infinite

a. A= (xlx € W and x > 3) = (4, 5, 6,...) Ā= (3, 2, 1, 0) b. A= (0, 1, 2,...) Ā= (-1, -2, -3,...)

Write an argument showing that the set of whole numbers can be placed in one to one correspondence with the set of natural numbers.

W= ( 0, 1, 2, 3...). X. N= ( 1, 2, 3, 4...). X+1. = N ~ W

For sets A and B, tell how you would show that A ₵ B.

Draw a venn diagram with one circle labeled "A" and the other "B." Put a dot inside circle A.

Write the following set using the listing (roster) method or set-builder notation. The set of natural numbers more than 20.

(20, 21, 22, 23, 24,...)

Name 2 infinite sets that are equivalent but not equal.

1. Set of natural numbers and the set of whole numbers 2. Set of even numbers and the set of odd numbers

A student asks if A is a subset of B and B is a subset of C, do we know that A is a subset of C? How do you respond?

Draw a small circle labeled "A," then draw a bigger one around of it labeled "B," and draw another circle around it labeled "C."