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