You can put this solution on YOUR website!
I'll assume that these particular F and T symbols do not represent "false" and "true", but rather just any logical statement. Your professor should have chosen different letters.
Another way to do the derivation is to use an indirect proof (aka proof by contradiction)
Number
Statement
Line(s) Used
Reason
1
H & (C & T)
2
~( ~F & T )
:.
F
3
~F
Assumption for Indirect Proof
4
~(~F) v ~T
2
De Morgan’s Law
5
F v ~T
4
Double Negation
6
~T
5, 3
Disjunctive Syllogism
7
(H & C) & T
1
Association
8
T & (H & C)
7
Commutation
9
T
8
Simplification
10
T & (~T)
9, 6
Conjunction
11
F
3 - 10
Indirect Proof
Line 3 is where we assume the opposite of the conclusion we want to arrive at.
From there a chain event of dominoes fall over to lead to T & (~T) which is a contradiction. One of T or ~T is false, while the other is true. This contradiction means our assumption must be the opposite.
The assumption ~F led to a contradiction, which means the opposite (F) must be a valid conclusion.
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