Asked by Danielle Crosby on May 08, 2024
Verified
Which disjunctive proposition is equivalent to this hypothetical proposition? If and only if p, then q.
A) p or q
B) p or not q
C) not p or not q
D) not p or q
E) ( p or not q) and (not p or q)
Disjunctive Proposition
A statement in logic that presents two or more alternatives, where the truth of at least one of the options implies the truth of the proposition.
Hypothetical Proposition
A conditional statement expressing a hypothesis and a consequence.
- Pinpoint and create converse, contrapositive, and equivalent claims in logical statements.
- Absorb the ramifications of presupposed, unequivocal, and alternative propositions.
Verified Answer
JL
Jacob LiaromatisMay 11, 2024
Final Answer :
E
Explanation :
The correct equivalent disjunctive proposition to "If and only if p, then q" is "(p or not q) and (not p or q)." This is because an "if and only if" statement is true only if both statements have the same truth value, which is captured by the combination of these two disjunctive propositions.
Learning Objectives
- Pinpoint and create converse, contrapositive, and equivalent claims in logical statements.
- Absorb the ramifications of presupposed, unequivocal, and alternative propositions.
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