Practice question · Select all that apply
Select every proposition that is logically equivalent to 'if p then q'.
Hints
- Build the truth table of 'if p then q' first — it is T, T, F, T — and compare each candidate against it column by column.
- One candidate is the converse and one is the contrapositive; only one of those two is equivalent.
Show the answer
- D. (NOT p) OR q
- E. if (NOT q) then (NOT p)
Why
'not p or q' and the contrapositive 'if not q then not p' both give T, T, F, T. The converse 'if q then p' gives T, F, T, T, which differs on two rows, and the two conjunctions are true on at most one row. Treating the converse as equivalent is the classic error the lesson names.
Practise Propositional Logic
The app has 8 more questions on this lesson, and keeps your place in the course. Computer Science I is free to start.