Practice question · Sort into groups
Sort each conditional by its truth value. Use the real arithmetic facts.
Groups: True · False
- If 2 + 2 = 5 then 3 is odd
- If 2 + 2 = 5 then 1 = 2
- If 2 + 2 = 4 then 1 = 2
- If 2 + 2 = 4 then 3 is odd
Hints
- Evaluate the hypothesis and the conclusion separately, then apply the one false row.
- A false hypothesis makes the whole implication true, whatever follows it.
Show the answer
True: If 2 + 2 = 4 then 3 is odd, If 2 + 2 = 5 then 3 is odd, If 2 + 2 = 5 then 1 = 2
False: If 2 + 2 = 4 then 1 = 2
Why
Only c4 has a true hypothesis with a false conclusion, so only c4 is false. c2 and c3 are vacuously true because 2 + 2 = 5 is false, an implication with a false hypothesis is always true, however absurd its conclusion.
Practise Implication and Equivalence
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