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#### Chapter 6

##### Section 6.2

1. a. $\left(\left(¬P\right)\wedge Q\right)\to \left(P\vee R\right).$

c. $A\to \left(B\vee \left(\left(\left(¬C\right)\wedge D\right)\wedge E\right)\right)\right)\to F.$

2. a. $\left(P\vee Q\to ¬R\right)\vee ¬Q\wedge R\wedge P.$

3. $\left(A\to B\right)\wedge \left(¬A\to C\right)\text{\hspace{0.17em}}or\text{\hspace{0.17em}}\left(A\wedge B\right)\text{\hspace{0.17em}}\vee \text{\hspace{0.17em}}\left(¬A\wedge C\right).$

5. $A\wedge ¬B\to False\equiv ¬\left(A\wedge ¬B\right)\vee False\equiv ¬\left(A\wedge ¬B\right)\equiv ¬A\vee ¬¬B\equiv ¬A\vee B\equiv A\to \mathrm{B.}$

7. a. If B = True, then the wff is true. If B = False and A = True, then the wff is false.

c. If A = True, then the wff is true. If A = False and C = True, then the wff is false.

e. If B = True, then the wff is true. If B = False and A = C = True, then the wff is false.

8. a. If C = True, A → C is true, so the wff is trivially true too. If C = False, then the wff becomes (A → B) ∧ (B → False) (A → False), which is equivalent ...

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