**1. a.** $((\neg P)\wedge Q)\to (P\vee R)\mathrm{.}$

**c.**
$A\to (B\vee (\left(\right(\neg C)\wedge D)\wedge E\left)\right))\to F\mathrm{.}$

**2. a.**
$(P\vee Q\to \neg R)\vee \neg Q\wedge R\wedge P\mathrm{.}$

**3.** $(A\to B)\wedge (\neg A\to C)\text{\hspace{0.17em}}or\text{\hspace{0.17em}}(A\wedge B)\text{\hspace{0.17em}}\vee \text{\hspace{0.17em}}(\neg A\wedge C)\mathrm{.}$

**5.** $A\wedge \neg B\to False\equiv \neg (A\wedge \neg B)\vee False\equiv \neg (A\wedge \neg B)\equiv \neg A\vee \neg \neg B\equiv \neg A\vee B\equiv A\to \mathrm{B.}$

**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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