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(a) p ∧ (¬q)The plane is on time and the sky is not clear (b) q → (p ∨¬p)If the sky is clear, then either the plane is on time or not (c) p ↔ qthe plane is on time if and only if the sky is clear 2 Construct a truth table for each propositionDisjoint (there are no interpretations under which both Q and ¬Q are true), it follows that M(P)∩M(¬Q) = Therefore there are no interpretations under which P is true and Q is false, and so P → Q is true under all interpretations M(P → Q) = M(True)Q ù* æloVhwT ¬ Q Q t b 6U ù*x z p ¯U tw T Ì TpsM Ôùtz ¢ £F M 0 ÅwÝ D ó w U ^ ¯q^ oS z hz¶ Í
Iii ¤U¸ü´CÅé51 ±qDirect oZn¤U¸ü52Qw È U bM \ ¬ Q ËloM { Ê ëq`oxz qz h åq Ê ëqw§M Ëjz {ü ¨ Ú « qtz þÂq ¨ ¯ {¬ q¬ ½ tx£ z ¤ ¬ ½ z ଠ½ z ü UK zf g w¢ Ê ¬ ½ ª ¢ Ê U áæ æO¬ ¬æ qz ¢ Ê U `ozáæ ½ t W`oM ¬ ½ Ê ëUáPropositional calculus is a branch of logicIt is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zerothorder logicIt deals with propositions (which can be true or false) and relations between propositions, including the construction of arguments based on them Compound propositions are formed by connecting propositions by
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