Thread: Cardinality of sets

I'm having some trouble figuring out how to find the cardinality of some sets. I've figured some of the problems out, but some I can't get.

Suppose |A| = 24, |B| = 21, |A U B| = 37, |A intersect C| = 11, |B-C| = 10, and |C-B| = 12. Find

A) |A intersect B|
C) |B-A|
D) |B U C|

For A), I came up with 8, for C) I came up with 13 ( is |B-A| = |A U B| - |A|?) and I have no idea how to start D).

Originally Posted by monsieur fatso

I'm having some trouble figuring out how to find the cardinality of some sets. I've figured some of the problems out, but some I can't get.

Suppose |A| = 24, |B| = 21, |A U B| = 37, |A intersect C| = 11, |B-C| = 10, and |C-B| = 12. Find

A) |A intersect B|
C) |B-A|
D) |B U C|

For A), I came up with 8, for C) I came up with 13 ( is |B-A| = |A U B| - |A|?) and I have no idea how to start D).

You're right for A) and C), except for C) I'd probably use |B - A| = |B|-|A intersect B|

For D)

Note that |B - C| = |B| - |B intersect C|
=> 10 = 21 - |B intersect C|
=> |B intersect C| = 11

also note |C - B| = |C| - |B intersect C|
=> 12 = |C| - 11
=> |C| = 23

Finally,
|B U C| = |B| + |C| - |B intersect C|
=> |B U C| = 21 + 23 - 11
=> |B U C| = 33

I'm a little rusty on this, so there's probably a shorter way to do this, fiddle around with it some more and see