Discrete Math: Sets and Cardinality

Question

Find the cardinality of each indicated set. Assume Ν₀={0,1,2,3...}

A = {n∈Ζ ; |n| < 84}

|A| = ?

B = {n∈A ; n=3m for some m∈Ν₀} Note that A is the set defined above.

|B| = ?

I'm kind of confused with this problem. I thought the answer would be 84 for A since its positive integers less that 84, and B would be 29 using the definition of A. However my teacher said this is wrong. Any help, hints, or insight would be greatly appreciated!

Answer 1

Joe

Z is the set of all integers (positive, negative, and zero).

So set A will contain { -83, -82, -81, .... -1, 0, 1, 2, .... , 83 } So the cardinality will be 2 x 83 + 1 = 167.

N subscript 0 is the set { 0, 1, 2, 3, 4 ... }

B will be the set { 0, 3, 6, 9, ...., 81 } so the cardinality is 28.

Mike