L> review 1.2 Conditional Statement forms Conditional explanation | definitions | depiction of If-Then as Or Negation, Converse & inverse | truth Table for Conditional explanation Conditional StatementsIn conditional statements, "If ns then q" is denoted symbolically through "p q"; p is called the hypothesis and also q is dubbed the conclusion. Because that instance, consider the two complying with statements: If Sally overcome the exam, climate she will get the job. If 144 is divisible by 12, 144 is divisible by 3. Let ns stand because that the explanation "Sally passes the exam" and also "144 is divisible through 12". allow q was standing for the statements "Sally will acquire the job" and also "144 is divisible by 3". The theory in the an initial statement is "144 is divisible by 12", and also the conclusion is "144 is divisible by 3". The 2nd statement says that Sally will gain the job if a particular condition (passing the exam) is met; it states nothing around what will happen if the condition is not met. If the problem is not met, the reality of the conclusion can not be determined; the conditional explain is because of this considered to be vacuously true, or true by default.

D E F i N ns T i O N SLet p and also q be statement variables which use to the adhering to definitions. Conditional: The conditional of q by ns is "If p then q" or "p suggests q" and also is denoted by ns q. That is false once p is true and also q is false; otherwise that is true. Contrapositive: The contrapositive that a conditional explain of the form "If p then q" is "If ~q climate ~p". Symbolically, the contrapositive of ns q is ~q~p. A conditional statement is logically equivalent to that contrapositive. Converse: mean a conditional declare of the form "If ns then q" is given. The converse is "If q then p." Symbolically, the converse of p q is q p. A conditional declare is no logically tantamount to its converse. Inverse: suppose a conditional statement of the kind "If ns then q" is given. The station is "If ~p climate ~q." Symbolically, the train station of p q is ~p ~q. A conditional explain is not logically identical to its inverse. just if : ponly if q method "if not q then not p, " or equivalently, "if p then q." Biconditional (iff): The biconditional of p and q is "p if, and also only if, q" and is denoted p q. That is true if both p and q have the same truth values and is false if p and q have opposite fact values. sufficient condition: p is a sufficient condition for q method "if ns then q." important condition: p is a necessary condition for q means "if not p then no q." In expressions the include and other logical operators such as , , and ~, the stimulate of operations is that is performed last while ~ is perform first.

Representation that If-Then as Or permit ~p it is in "You perform your homework" and q it is in "You will flunk". The offered statement is "Either you carry out your homework or you will flunk", i m sorry is ~p q. In if-then form, p q way that "If you execute not perform your homework, then you will certainly flunk", whereby p (which is identical to ~~p ) is "You execute not do your homework".


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p q ~p q
The negative of a conditional explain is represented symbolically as follows: ~(p q) p ~q By definition, p q is false if, and also only if, that hypothesis, p, is true and its conclusion, q, is false.The converse and also inverse of a conditional statement are logically indistinguishable to every other, however neither the them are logically identical to the conditional explain
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practice Exercises
Truth Table because that Conditional Statements ns q p q q ns p q (p q) (q p) T T T T T T T F F T F F F T T F F F F F T T T T The fact values of ns q is tantamount to (p q) (q p).