Question 1011177
I need to help on the following proofs 

Proof 1 
<pre>
1. B &#8743; F 
2. ¬(B &#8743; G) 
   ------ 
        ¬G 

3. ~B v ~G          2, DeMorgan
4. B               1, Simplification
5. ~~B             4, Double negation
6. ~G              3,6, Disjunctive syllogism 

</pre>
Proof 2
<pre> 
By truth table:

Go through the first time with small letters t and f
Go through the second time with 1's for T and 0's for F 
Go through the third time with + for T and - for F

Goal - [A &#8594; (B &#8594; C)] &#8596; [(A &#8594; B) &#8594; (A &#8594; C)] 
        T 1  T t T   +   T t T  1  T t T
        T 0  T f F   +   T t T  0  T f F
        T 1  F t T   +   T f F  1  T t T
        T 1  F t F   +   T f F  1  T f F
        F 1  T t T   +   F t T  1  F t T
        F 1  T f F   +   F t T  1  F t F
        F 1  F t T   +   F t F  1  F t T
        F 1  F t F   +   F t T  1  F t F

As we see there are only +'s under the &#8596; so the 
equivalence holds
</pre>
Proof 3 
<pre>
I have never studied how to do proofs like the third one.
What is it called?  I'll google it and learn what it's all
about.
</pre>

&#8707;x (A(x) &#8744; B(x)) 
&#8707;x A(x) &#8594; &#8704;x (C(x) &#8594; B(x)) 
&#8707;x C(x) 
Goal &#8707;x B(x)

Edwin</pre>