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I need someone to tell me if I answered these questions correctly and if not explain what I did wrong. My answers are in bold.

1. Indicate which of the following are true and which are false in an interpretation in which A and B are false and C is true.

a) (A v (B ^ C)) (

b) (-A ^ (B v C)) (

c) ((A v B) ^ C) (

d) (-(A ^ B) ^ C) (

e) (C -> (A -> B)) (

f) (A -> (C -> B))) (

g) (-A -> (A <-> B)) (

h) ((A <-> B) <-> C) (

i) ((A <-> -B) <-> (B <-> -A)) (

j) (((A ^ C) -> B) <-> (B -> (A ^ C)) (

2. Draw a complete truth-table for the following sentence and indicate whether it is valid or invalid.

(((B ^ C) -> A) <-> ((B -> A) v (C -> A)))

I think it's

1. Indicate which of the following are true and which are false in an interpretation in which A and B are false and C is true.

a) (A v (B ^ C)) (

**false**)b) (-A ^ (B v C)) (

**true**)c) ((A v B) ^ C) (

**false**)d) (-(A ^ B) ^ C) (

**true**)e) (C -> (A -> B)) (

**false**)f) (A -> (C -> B))) (

**false**)g) (-A -> (A <-> B)) (

**false**)h) ((A <-> B) <-> C) (

**true**)i) ((A <-> -B) <-> (B <-> -A)) (

**true**)j) (((A ^ C) -> B) <-> (B -> (A ^ C)) (

**false**)2. Draw a complete truth-table for the following sentence and indicate whether it is valid or invalid.

(((B ^ C) -> A) <-> ((B -> A) v (C -> A)))

I think it's

**Invalid**
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