201409 Math 122 Solutions Ideas for Midterm 2 Practice Questions
1. () Suppose A B = A B. We show A B and B A. Take any x A.
Then x AB. Since AB = AB, we have x AB. Therefore x B, and
A B. The same argument with A and B exchanged shows B A. Therefore
A=B
201409 Math 122 Assignment 3 Solution Ideas
1. (a) Let t S. Since t can be rotated through 0 (or any multiple of 360) degrees to be identical to t,
R is reexive.
Now suppose t1 , t2 S and t1 Rt2 . Then t1 can be rotated to be identical to t2 . The opposit
201409 Math 122 Assignment 4 Solution Ideas
1. (a) If X1 is nite, then list its elements followed by those of X2 . If X1 is innite and
X2 is nite, then list the elements of X1 followed by those of X1 . Suppose both
sets are innite. Then there is a sequenc
201409 Math 122 Assignment 1 Solution Ideas
1. Let p be the statement the goods are satisfactory, and q be the statement the money
is refunded. Then the given statement is p q. It is logically equivalent to p q
(the second statement) and to its contraposi
201409 Math 122 Assignment 2 Solution Ideas
1.
A \ (B \ C)
=
=
=
=
=
A (B \ C)c
A (B C c )c
A (B c C)
(A B c ) (A C)
(A \ B) (A \ C c )
2. Take any (a, c) A C. Then a A and c C. Since A B and C D, a B and c D.
Therefore (a, c) B D, so A C B D. It remains
Solution Ideas for Math 122 Practice Midterm 1
Questions
1. Converse: If Gary goes cycling or running then it is not raining and not
windy.
Contrapositive: If If Gary goes does not go cycling and does not go running then it is raining or windy
3
2. When x
201409 Math 122 Practice MT 3 Solution Ideas
1. (a)
(b)
(c)
(d)
Countable (nite)
Countable (subset of a countable set)
Uncountable (non-empty interval of real numbers)
Uncountable (if countable, then R = Q (R Q) is the union of 2
countable sets, and hence
Function denitions: Generalizing from the real-valued case
Real-valued functions of a real variable (denitions we know)
A function f : R R is a subset f R R such that every x R appears at most once as
the rst component of an ordered pair in f .
When (x,