Are the following two propositions equivalent?
p IMPLIES (q IMPLIES r)
p IMPLIES (q AND r)
From what I can tell, using the logical equivalences, this should be false, correct?
p IMPLIES (q IMPLIES r)
(p IMPLIES q) IMPLIES r
This one should be true, correct?
(p IMPLIES q) AND (NOT p IMPLIES q) is equivalent to q
I believe this one is true. Is that right?
Thanks in advance!
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$\begingroup$The first pair are not equivalent. Take $p,r$ true, $q$ false: the first formula is true, the second is false.
The second pair are not equivalent. Take $p, r$ false, $q$ true: the first formula is true, the second is false.
The third statement is valid, yes.
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