In logic, shorthand such as p\u2192q is used; it means “p implies q.” p\u00a0\u2228 q means “p or q.” p\u00a0\u2227 q means “p and q”. \u00acp means “not p”. p, q would each stand for a statement such as “It’s raining” or “The date is Feb 12”.<\/p>\n
p\u2192q can be true or false depending on the values of p and q. If they are both false, for instance, p\u2192q is true, since q is in the same state as p. If p is false but q is true, p\u2192q is true.<\/strong> Perhaps surprising, the reasoning for this case is that q is true regardless of p; whatever p is, it implies q. If p is true but q is false, p\u2192q is false, because p’s being true fails to make q also true. Lastly, and intuitively, if both are true then p\u2192q is true. Often, 0 is used for false, 1 for true.<\/p>\n A compound statement is two or more statements linked by one or more “ands” or “ors”. Therefore, p\u00a0\u2228 q is a compound statement. To return to the possible values for p, q, proposed in the first paragraph, we have<\/p>\n p\u00a0\u2228 q means “It’s raining or the date is Feb 12.”<\/p>\n Regardless of the meanings of p, q, in a given case, p\u00a0\u2228 q is true when one or both are true; p\u00a0\u2227 q is true only when both p, q, are true.<\/p>\n ⊻ means “exclusive or”. p ⊻ q is true when exactly one of p, q, is true (not both).<\/p>\n I’ll be talking more about logic in future posts:)<\/p>\n Source:<\/p>\n Grimaldi, Ralph P. Discrete and Combinatorial Mathematics<\/u>. Don Mills: Addison-
Wesley, 1994.<\/p>\n