Euler Circles and Logic Questions

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Essay #: 060267
Total text length is 1,940 characters (approximately 1.3 pages).

Excerpts from the Paper

The beginning:
Euler Circles and Logic Questions
B
A
C1.Determining the validity of the statements using Euler circles.
A)No A is B
Some C is A
___________
Some C is not B
B)All B is A
All C is A
A
___________
All C is B
C
B
Basic Connectives
A is p
B is q
C is r
A)No A is equivalent to B to p ~q
All C is A is equivalent to r p
Some C is B is equivalent to
r^q
B)All B is equivalent to A to q p
All C is equivalent to A to r p
All C is equivalent to B to r q
Truth Tables
A)
A
B
C
[a ~b) ^ (c ^ a) (c ^ b)
T
T
T
T F
F
F
T
T
T
T
T
F
F
T
T
F
T F
F
F
F
F
T
T
F
F
F
T
F
T
T
T
T
T
T
T
T
T
T
T
T
T
F
F
T
T
T
F
F
F
T
T
F
F
T
F
T
T
F T F
F
F
T F T
T
F
F
F
T
F
F T F
F
F
F
F
T F
F
F
F
F
T
F T
T
F T F
F
T
T
T
T
F
F
F
F T
T
F
F
F
F
T F T
T
B
A
B
C
[a b) ^ (C A) (C B)
T
T...
The end:
.....l q.
3.In this question we are asked to create a circuit that can be turned on or off from either end of the hall. To do this we need to create a parallel circuit. A parallel circuit will work as long as one of the switches is closed.
A series circuit would not work because both switches would need to be on closed for the circuit to work.
This argument can be made in two ways. On an intuitive level it can be seen if you close one switch you create a complete circuit.
This argument can also be proven using a truth table. For example:
P
Q
P v Q
P
Q
P V Q
T
T
T
Closed
Closed
Current
T
F
T
Closed
Open
Current
F
T
T
Open
Closed
Current
F
F
F
Open
Open
No Current
Bibliography
Bluman
, Allan G.(2005), Mathematics in Our World, Boston:
McGraw-Hill.