Let A, B, C, D, and E be statements. Consider the following
four statements made from these using the usual five sentential
connectives ~, ∨, &, →, and ↔ (explained below):
I: (((A&B)∨(B↔A))∨E)↔(((C↔(C∨&A)∨(E&A))
II: ((~((D∨((A&(D→∨((~C∨A)∨)∨E)∨E)&A)↔A
III: ((~A∨(C→A))&~C)→(B→(B→((((A∨B)&A)∨E)&A)))
IV: (A&(E→((E∨A)→E)))→((((E→A)↔D)↔(E↔C))∨E)
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Which of the following statements are derivable from
the above set of four statements, and which are not?
The five sentential connectives are:
1. ~ (not) ~X is true when X is false and ~X is false when X is true.
2. ∨ (or) X∨Y is true when at least one of X and Y is true, otherwise it is false.
3. & (and) X&Y is true when both X and Y are true; otherwise it is false.
4. → (implication) X→Y is true unless X is true and Y is false, in which case it is false.
5. ↔ (equivalence) X↔Y is true when X and Y have the same truth value, otherwise it is false.
In case someone would rather have the RPN version of the
statements, I include them below:
Question
superprismatic
Let A, B, C, D, and E be statements. Consider the following
four statements made from these using the usual five sentential
connectives ~, ∨, &, →, and ↔ (explained below):
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