CSC 133 Discrete Structures Quiz 1 Spring 2001

1. Complete the truth table.

p q	p Ú    (~p Ù q)    ®    p
T T	T	F	T	T
T F	T	F	T	T
F T	T	T	F	F
F F	F	F	T	F
	2	1	3

2. Doing his homework regularly is a necessary condition for Jim to pass the course.
   Let r = “Doing his homework regularly”, and s = “Jim to pass the course”.
1. Rewrite the sentence symbolically using the conditional (®).
   We have: r is necessary for s.
   Which translates to: ~r ® ~s.
   
   
   
2. Rewrite this if-then as an or.
   ~r ® ~s º r Ú ~s.
   
   
   
   
3. Use DeMorgan’s Law to write negations for:
1. The train is late and my watch is fast.
   We have p Ù q, where p = the train is late, q = my watch is fast.
   The negation is ~(p Ù q), which by DeMorgan’s Law is ~p Ú ~q.
   The train is not late or my watch is not fast.
2. The connector is loose or the machine is unplugged.
   We have p Ú q, where p = the connector is loose, q = the machine is unplugged.
   The negation is ~(p Ú q), which by DeMorgan’s Law is ~p Ù ~q.
   The connector is tight and the machine is plugged in.