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Kenneth Rosen Edition 7th Exercise 1.3 Question 6 (Page No. 34)
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Use a truth table to verify the first De Morgan law
$\sim(p \wedge q)$ $\equiv$ $\sim p \vee \sim q$
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Kenneth Rosen Edition 7th Exercise 1.6 Question 34 (Page No. 80)
The Logic Problem, taken from WFF'N PROOF, The Game of Logic, has these two assumptions:1. Logic is difficult or not many students like logic. 2. If mathematics is easy, then logic is not difficult. By translating ... not easy. That if not many students like logic, then either mathematics is not easy or logic is not difficult.
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Kenneth Rosen Edition 7th Exercise 1.3 Question 34 (Page No. 35)
Find the dual of each of these compound propositions. $p \vee \sim q$ $p \wedge(q \vee (r \wedge T))$ $(p \wedge \sim q) \vee( q \wedge F)$
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Kenneth Rosen Edition 7th Exercise 1.3 Question 15 (Page No. 34)
Determine whether $(\sim q \wedge (p \rightarrow q)) \rightarrow \sim p$ is a tautology.
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Kenneth Rosen Edition 7th Exercise 1.3 Question 7 (Page No. 34)
Use De Morgan’s laws to find negation of each of the following statements. Jan is rich and happy. Carlos will bicycle or run tomorrow. Mei walks or takes the bus to class. Ibrahim is smart and hard working.
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Kenneth Rosen Edition 7th Exercise 1.3 Question 5 (Page No. 34)
Use a truth table to verify the distributive law $p \wedge (q \vee r ) \equiv (p \wedge q ) \vee (p \wedge r).$
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Kenneth Rosen Edition 7th Exercise 1.3 Question 4 (Page No. 34)
Use truth tables to verify the associative laws. $(p \vee q) \vee r \equiv p \vee (q \vee r).$ $(p \wedge q) \wedge \equiv p \wedge(q \wedge r).$
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Kenneth Rosen Edition 7th Exercise 1.3 Question 3 (Page No. 34)
Use truth tables to verify the commutative laws $p \vee q \equiv q \vee p $ $p \wedge q \equiv q \wedge p $
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