Def. A compound proposition that is always true, no matter what the truth values of the (simple) propositions that occur in it, is called tautology. A compound proposition that is always false, no matter what, is called a contradiction. A proposition that is neither a tautology nor a contradiction is called a contingency. Q1) Let p be a proposition. Indicate whether the propositions are: (A) tautologies (B) contradictions or (C) contingencies. Proposition pV¬p pA-p X+7 = 18 for every real number x type Q2) Use truth tables to show that --p=p (the double negation law) is valid. Q3) Use truth tables to show that p v (p ^ q) = p _is valid. Q3) Use truth tables to show that p v (q A r) = (p V q) A (p V r) is valid. Q4) Without truth tables to show that ¬ (-p ^ q) =pV ¬q

Def. A compound proposition that is always true, no matter what the truth values of the (simple) propositions that occur in it, is called tautology. A compound proposition that is always false, no matter what, is called a contradiction. A proposition that is neither a tautology nor a contradiction is called a contingency. Q1) Let p be a proposition. Indicate whether the propositions are: (A) tautologies (B) contradictions or (C) contingencies. Proposition pV¬p pA-p X+7 = 18 for every real number x type Q2) Use truth tables to show that --p=p (the double negation law) is valid. Q3) Use truth tables to show that p v (p ^ q) = p _is valid. Q3) Use truth tables to show that p v (q A r) = (p V q) A (p V r) is valid. Q4) Without truth tables to show that ¬ (-p ^ q) =pV ¬q

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Advanced Engineering Mathematics

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Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Def. A compound proposition that is always true, no matter what the truth values of the
(simple) propositions that occur in it, is called tautology. A compound proposition that is
always false, no matter what, is called a contradiction. A proposition that is neither a
tautology nor a contradiction is called a contingency.
Q1) Let p be a proposition. Indicate whether the propositions are: (A) tautologies (B)
contradictions or (C) contingencies.
Proposition
pV-p
p^-p
X +7 = 18 for every real number x
type
Q2) Use truth tables to show that --p=p
(the double negation law) is valid.
Q3) Use truth tables to show that p V (p ^ q) = p is valid.
Q3) Use truth tables to show that p V (q A r) = (p V q) ^ (p V r) is valid.
Q4) Without truth tables to show that ¬
-(-p^q) =p V ¬q

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