## Tuesday, March 15, 2011

### Set theory practice.

I haven't put any set theory practice problems up on the website before because the editor software for this blog can't put up the symbols for union, intersection and complement in regularly typed sentences. So instead, I'm going to use the words union, intersect and -bar to take the place of those symbols. I'm also going to use A - B to mean A intersect B-bar, which means the stuff that is in A but is NOT in B.

U = {a, b, c, d, e, f}

P = {f, a, d, e}_____Card(P) = 4
Q = {c, a, b}_______Card(Q) = 3
R = {c, e, d, e, d}___ Card(R) = 3 (there are two copies of the letters e and d, but each only counts once)

Find the following sets and their cardinalities using the set operations we have learned in class.

P union Q = __________

Card(P union Q) = ______

P intersect R = __________

Card(P intersect R) = ______

P-bar union Q-bar = __________

Card(P-bar union Q-bar) = ______

(P union Q) intersect R = __________

Card((P union Q) intersect R) = ______

P union (Q intersect R) = __________

Card(P union (Q intersect R)) = ______

#### 1 comment:

Prof. Hubbard said...

U = {a, b, c, d, e, f}

P = {f, a, d, e}
Q = {c, a, b}
R = {c, e, d, e, d}

slight trick:
R = {c, e, d} is simpler.

Find the following sets and their cardinalities using the set operations we have learned in class.

P union Q = {a, b, c, d, e, f}

Card(P union Q) = 6

P intersect R = {d, e}

Card(P intersect R) = 2

P-bar union Q-bar = {b, c, d, e, f}

Card(P-bar union Q-bar) = 5

(P union Q) intersect R = {c, e, d}

Card((P union Q) intersect R) = 3

P union (Q intersect R) = {a, c, d, e, f}

Card(P union (Q intersect R)) = 5