- #1
robert
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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)) (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
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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