Project ForgeDiscrete Mathematics
Propositional Logic
GATE 2012
Medium
What is the correct translation of the following statement into mathematical logic?
"Some real numbers are rational"
- A∃x (real(x) ∨ rational(x))
- B∀x (real(x) → rational(x))
- ∃x (real(x) ∧ rational(x))
- D∃x (rational(x) → real(x))
Explanation
'Some' is an existential quantifier (∃x), and 'real numbers that are rational' requires BOTH properties to hold for that x simultaneously — a conjunction (∧), not a disjunction or implication. So the correct translation is ∃x (real(x) ∧ rational(x)).
Source: GATE CS 2012 (2012)
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