Question

Let’s assume these are the 25 coins that were collected:

1966 penny, 1967 nickel, 1966 quarter, 1967 penny, 1965 penny, 1966 half dollar, 1967 quarter, 1965 dime, 1967 dime, 1968 quarter, 1964 dime, 1966 nickel, 1965 nickel, 1967 half dollar, 1966 dime, 1964 nickel, 1969 quarter, 1969 half dollar, 1965 half dollar, 1968 penny, 1968 dime, 1964 quarter, 1965 quarter, 1969 dime, 1968 nickel

To simplify writing each coin out, let’s abbreviate 1966 penny by 6P, and 1967 nickel by 7N, etc. So in our collection, we have the following:

6P, 7N, 6Q, 7P, 5P, 6H, 7Q, 5D, 7D, 8Q, 4D, 6N, 5N, 7H, 6D, 4N, 9Q, 9H, 5H, 8P, 8D, 4Q, 5Q, 9D and 8N

A physical model for these coins is found on Material Card 1. If you haven't already done so, cut out a set of coins from this Material Card and use them to do several of the following exercises.

Let S be the subset of coins from 1964, V from 1965, W from 1966, X from 1967, Y from 1968, Z from 1969 and T from 1970.

Compute the following.

n(P) =   n(N) =    n(Q) =    n(D) =

n(Z) =    n(H) =    n(Y) =    n(T) =

n(S) =    n(W) =    n(X) =    n(V) =

n(C) =    n(A) = (A represents the one dollar coins in our set C)      

Answer 1

Given data:

6P, 7N, 6Q, 7P, 5P, 6H, 7Q, 5D, 7D, 8Q, 4D, 6N, 5N, 7H, 6D, 4N, 9Q, 9H, 5H, 8P, 8D, 4Q, 5Q, 9D and 8N

Let's understand what is n(A).

n(A) = number of elements in set A. Suppose, A={1,7,9} then n(A) = 3.

Let's compute the given:

n(P) => P = set containing pennies => P = {5P,6P,7P,8P} => n(P) = 4

n(N) => N = set containing nickels => N = {4N,5N,7N,6N,8N} => n(N) = 5

n(Q) => Q = set containing quaters => Q = {4Q,5Q,6Q,7Q,8Q,9Q} => n(Q) = 6

n(D) => D = set containing dollars => D = {{4D,5D,6D,7D,8D,9D} => n(D) = 6

n(Z) => coins from 1969 => Z = {9Q,9H,9D} => n(Z) = 3

n(H) => set containing half dollars => H = {5D,6D,7D,9D} => n(D) = 4

n(Y) => coins from 1968 => Z = {8Q,8P,8D,8N} => n(Y) = 4

n(T) => coins from 1970 => T = { } => n(T) = 0

n(S) => coins from 1964 => S = {4Q,4N,4D} => n(S) = 3

n(W) => coins from 1966 => W = {6P,6Q,6H,6N,6D} => n(Z) = 5

n(X) => coins from 1967 => X = {7P,7Q,7H,7N,7D} => n(X) = 5

n(V) => coins from 1965 => V = {5P,5Q,5H,5N,5D} => n(V) = 5

n(C) Here set C is not given, so we cannot anwer this. or we can say it is undefined.

n(A) => one dollar coins in our set C => Since we don't know C, we cannot answer this too.