Find the true and the false statements.

1. Either 2 and 3 are both false or 2 and 4 are both true.
2. Either 1 is false and 3 is true or 3 is false and 4 is true.
3. If and only if 2 is false, then either 1 or 4 is true.
4. Either 1 and 2 are both false or 3 and 4 are both true.

(In reply to Boolean by Charlie)

We denote statements 1 to 4 as S1, S2, S3 and S4 and indicate any probable false statement as F and mark any probable true statement as T.

Then the possiblilities are:

S1....S2....S3.....S4.....Is This Valid?
F.......F......F.......F........... NO
F.......F......F.......T........... NO
F.......F......T.......F........... NO
F.......F......T.......T........... NO
F.......T......F.......F........... NO
F.......T......F.......T........... NO
F.......T......T.......F........... YES
F.......T......T.......T........... NO
T.......F......F.......F........... NO
T.......F......F.......T........... NO
T.......F......T.......F........... NO
T.......F......T.......T........... NO
T.......T......F.......F........... NO
T.......T......F.......T........... NO
T.......T......T.......F........... NO
T.......T......T.......T........... NO

From the above table, it is evident that the statements 1 and 4 are false while the statements 2 and 3 are true.

Edited on May 18, 2007, 5:53 am

Posted by K Sengupta on 2007-05-18 05:50:56