Practice question · Select all that apply
Select every statement that is logically EQUIVALENT to 'if p then q'.
Hints
- Two of these have exactly the same truth table as the original.
- One is the contrapositive; the other rewrites the conditional using OR.
Show the answer
- C. (NOT p) OR q
- E. if NOT q then NOT p
Why
The contrapositive 'if NOT q then NOT p' and the disjunctive form '(NOT p) OR q' both match the implication row for row. The converse and inverse are not equivalent, and 'p AND (NOT q)' is its NEGATION, the one case where the implication fails.
Practise Implication and Equivalence
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