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=====Converse Implication,  Discrete=====


====Definition====
For any two propositions P and Q, if Q implies P, then P is the converse implication of Q.

It may take the following forms:

  - p⊂q 
  - Bpq
  - p←q

   P  |  Q  | XNq  
   _  _  _  _  _  
   0  |  0  |  0 
   0  |  1  |  0 
   1  |  0  |  1 
   1  |  1  |  0
====References====
List any sites, books, or sources utilized when researching information on this topic. (Remove any filler text).

  * http://en.wikipedia.org/wiki/Converse_implication
  * http://www.jimloy.com/logic/converse.htm
  * http://www.millersville.edu/~bikenaga/math-proof/truth-tables/truth-tables.html

=====Discrete Keyword Phase 2=====
Nonconjunction/Not Both ... And.

====Definition====
The relation among the components of such a proposition, usually expressed by AND or & or ·
====References====
  * http://dictionary.reference.com/browse/non-conjunction
  * http://en.wikipedia.org/wiki/Conjunction_(grammar)
  * http://philosophy.lander.edu/logic/conjunct.html
=====Discrete Keyword 1 Phase 2 Phase 2=====
Left Projection

====Definition====
The left-shift operator causes the bit pattern in the first operand to be shifted to the left by the number of bits specified by the second operand. The value of a left-shift expression x << y is x * 2y

====References====

  * Chapter 2: Types, Operators, and Expressions. The C Programming Language Book.
  * http://en.wikipedia.org/wiki/Bitwise_operation
  * http://msdn.microsoft.com/en-us/library/336xbhcz.aspx
  * http://msdn.microsoft.com/en-us/library/f96c63ed(v=vs.80).aspx


====Demonstration (Left Projection)====

<code c>
/*
 * Sample code block
 */
#include <stdio.h>

int main()
{
  unsigned int i;
  int j;
  int input;

  i = 1;

printf("Enter a number to end your projection on: ");
scanf("%d", &input);

  for(j = 0; j < input ; j++)
{
    i = i << 1;
    printf("Left shift %d: %d(%X)\n", j, i);
}

return (0);
}

</code>

Alternatively (or additionally), if you want to demonstrate something on the command-line, you can do so as follows:

<cli>
lab46:~$ cd ./src/discrete
lab46:~/src/discrete$ ls
big  bigl  bigl.c  bignum.c  bit  bitwise.c  ctruth  ctruth.c  inc  inc.c  sets.c  sort  sort.c
lab46:~/src/discrete$ ./bit
Enter a number to end your projection on: // Choose any number here \\ 9
Left shift 0: 2(0)
Left shift 1: 4(1)
Left shift 2: 8(2)
Left shift 3: 16(3)
Left shift 4: 32(4)
Left shift 5: 64(5)
Left shift 6: 128(6)
Left shift 7: 256(7)
Left shift 8: 512(8)
</cli>

    Numbers in ( ) represent hexadecimal format, for when it becomes applicable at larger projection numbers.
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