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IF ... THEN ... ELSE--unlike implication--does not evaluate to an ambiguous "TRUTH" when the first proposition is false i.e. c = F in (c -> b). For example, most people would reject the following compound proposition as a nonsensical non sequitur because the second sentence is not connected in meaning to the first.
: Example: The proposition " IF 'Winston Churchill was Chinese' THEN 'The sun rises in the east' " evaluates as a TRUTH given that 'Winston Churchill was Chinese' is a FALSEHOOD and 'The sun rises in the east' evaluates as a TRUTH.

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