Below is the solutions to the even problems for assignment #1...
2a. No 2b. No 2c. Proposition, False 2d. No 2e. Proposition, False 2f. No
4a. Jennifer and Teja are not friends. 4b. There are not 13 items in a baker's dozen. 4c. Abby did not send more than 100 text messages every day. 4d. 121 is not a perfect square.
6a. True 6b. True 6c. False 6d. false 6e. False
32a/b
| p | p' | 32a. p -> p' | 32b. p <-> p' |
|---|---|---|---|
| T | F | F | F |
| F | T | T | F |
32c/d/e/f
| p | q | 32c. p xor ( p or q ) | 32d. ( p and q ) -> ( p or q ) | 32e. ( q -> p' ) <-> ( p <-> q ) | 32f. ( p <-> q ) xor ( p <-> q' ) |
|---|---|---|---|---|---|
| T | T | F | T | F | T |
| T | F | F | T | F | T |
| F | T | T | T | F | T |
| F | F | F | T | T | T |
44a.
0 1011
or 1 1011
----------
1 1011
and 1 1000
----------
1 1000
44b.
0 1111
and 1 0101
----------
0 0101
or 0 1000
----------
0 1101
44c.
0 1010
xor 1 1011
----------
1 0001
xor 0 1000
----------
1 1001
44d.
1 1011 1 0001
or 0 1010 or 1 1011
---------- ----------
1 1011 1 1011
and 1 1011 <-----+
----------
1 1011
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