Which of the following options correctly represents the symbolic form of the…
2025
Which of the following options correctly represents the symbolic form of the given statement ?
"For all x, x < 5 or x ≥ 5"
(Where :
• P(x) represents x < 5
• Q(x) represents x ≥ 5)
- A.
∀x[P(x) ∨ Q(x)]
- B.
∃x[P(x) ∨ Q(x)]
- C.
∀x[P(x) ∧ Q(x)]
- D.
∃x[P(x) ∧ Q(x)]
Attempted by 41 students.
Show answer & explanation
Correct answer: A
The statement begins with 'For all x', which translates to the universal quantifier ∀x. The phrase 'or' indicates logical disjunction, represented by ∨. Since P(x) is x < 5 and Q(x) is x ≥ 5, the full symbolic form is ∀x[P(x) ∨ Q(x)].