For each of the following pairs of sets determine whether th

For each of the following pairs of sets, determine whether the two given sets A and B have the same cardinality. (Enter Y for yes, N for no) A = {a, b, c, d, e}, B = {-7, -5, -3, -1} A = {3k + 1: k Z and 1 lessthanorequalto k lessthanorequalto 10}, B = {5k - 1: k Z and 1 lessthanorequalto k lessthanorequalto 10} A = {1, 2}, B = P({1, 2}) A = {n Z:n is even}, B = {n Z: n is odd}

Solution

1. Yes

A and B are finite sets with 5 elements each. So they have the same cardinality

2. Yes

A and B are finite set with 10 elements each. So they have the same cardinality

3. No

A is a finite set with cardinality 2

P is its power set with cardinality 2^2=4

4. Yes

f(n)=n+1 gives a bijective map from A to B

HEnce they have the same cardinality