(P ^ Q) => P named Simplification meaning if (P ^ Q) then P
(P ^ Q) => Q named Simplification meaning if (P ^ Q) then P
If the compound statement (P ^ Q) => P is given and is true (it is always true) and P ^ Q is true then P must be true. (see truth table to follow the reasoning).
The same reasoning applies to (P ^ Q) => Q.
P = I cannot get hold of any money
Q = The bank will not lend me any money
The the compound statement: “if I cannot get hold of any money and the bank will not lend me any money then I cannot get hold of any money” is always true.
Suppose that, it is true that (P) I cannot get hold of any money
Suppose that, it is true that (Q) The bank will not lend me any money
Then we can conclude that it is true that: “I cannot get hold of any money – if I cannot get hold of any money and the bank will not lend me any money”. You can see that just more truth (The bank will not lend me money) to some original truth (I cannot get hold of any money) – So we can take it that the original truth is still true if both the original truth (I cannot get hold of any money) and the added truth (the bank will not lend me any money) are both true.
3 no namers – logical implications
Hypothetical Syllogism – a logical implication
Disjunctive Syllogism – a logical implication
Simplification – a logical implication
Addition – a logical implication
Modus tollens – a logical implication
Modus ponens – a logical implication
Logical Implications
Discrete Mathematics for Dummies 