Simple argumentative, existential claims form the basis of math or symbolic logic. Existential refers to statements about something as it exists in the world. For example; "John is a bachelor" is an existential claim about the world, as it posits a theory or argument about some element of the world, namely the marriage status of John. Premises and conclusions build up simple argumentative claims. When taken in conjunction, premises are the statements that prove a conclusion, which is the proven truth of a number of premises. For example; "1. Bachelors are unmarried men. 2. John is a Bachelor. 3. Therefore, John is an unmarried man." In this sentence, "1" and "2" represent premises, while "3" represents the conclusion.
Upon introducing the simplest elements of an argument -- premises and conclusions -- it is important to establish the basic symbols most often deployed and understood by mathematical logicians, in this case "P" and "Q." "P," aptly, symbolizes "premise," while "Q," confusingly, symbolizes "conclusion." Additionally, premises tend include numbers alongside the P, while conclusions tend to receive additional, subsequent letters. For example; P1, P2, P3 for first, second and third premise, and Q, R, S for first, second and third conclusion. Though many theories exist about the etymological significance of P and Q as the common letters of math logic -- from the statement "mind your Ps and Qs" to possible abbreviations of the Latin terms "per" and "quod" -- none truly accounts or explains why P and Q are so commonly considered the basic symbolism of premise and conclusion.
Math and symbolic logic tends to rely upon If/Then connected structures for arguments, rather simple assertions of premises. For example; rather than "P1: Bachelors are unmarried men. P2: John is a Bachelor. Q: John is an unmarried men," a math or symbolic logic representation of the same argument would substitute accordingly: "P1: If Bachelors are unmarried men, and P2: If John is a bachelor, then Q: John is an unmarried man. P1 is true and P2 is true, therefore Q" This further substitutes as If P1 and P2, then Q. P1 and P2, therefore Q.
The final stage in introducing math or symbolic logic requires the substitution of further symbols so as to completely eliminate any written words. While some mathematical or symbolic logicians employ simple mathematical symbols such as "+," "-" and "=," others employ highly specific symbols unique to math or symbolic logic as a discipline. For the purposes of your presentation, consider using symbols with which your audience is already familiar. For example; rewrite "If P1 and P2, then Q. P1 and P2, therefore Q" as "P1+P2 = Q. P1. P2. Q." Using capital letters to emphasize the meaning of this symbolic logical argument, these symbols read: "IF Bachelors are unmarried men, AND John is a bachelor, THEN John is an unmarried man. Bachelors ARE unmarried men. John IS a bachelor. THEREFORE, John IS an unmarried man."