Translating English into logic
Four patterns cover most sentences. Two common mistakes look almost right.
T∀x (Cube(x)→Small(x))
1 of 4
How it works
“Every A is B” becomes ∀x (A(x) → B(x)). “Some A is B” becomes ∃x (A(x) ∧ B(x)). The connective changes with the quantifier.
Swap them and the sentence still parses, but it says something else. The board below shows each mistake failing.
- Every cube is small.∀x (Cube(x)→Small(x))
- Some cube is small.∃x (Cube(x)∧Small(x))
- No cube is small.¬∃x (Cube(x)∧Small(x))
- Only cubes are small.∀x (Small(x)→Cube(x))
Worth memorizing
Every → ∀ with →.
Some → ∃ with ∧.
“Only A are B” flips the arrow.
It means every B is an A: ∀x (B(x) → A(x)).
Practice
0 of 4 rightQuestion 1
“Every tetrahedron is large.”
Question 2
“Some cube is left of a.”
Question 3
“No dodecahedron is small.”
Question 4
“Only cubes are large.”