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Kenneth Rosen Edition 7th Exercise 1.3 Question 7 (Page No. 34)
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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 1.7 Question 34 (Page No. 91)
Is this reasoning for finding the solutions of the equation $\sqrt{2x^2−1=x}$ correct? $\sqrt{2x^2−1=x}$ is given; $2x^2−1=x^2$, obtained by squaring both sides of (1); $x^2−1=0$, obtained by subtracting $x^2$from both sides of (2); ... lefthand side of$x^2−1$; $x=1$ or $x=−1$,which follows because $ab=0$ implies that $a=0$ or $b=0$
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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 6 (Page No. 34)
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 1.3 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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